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Journal articles on the topic 'Curvature properties'

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Author: Grafiati

Published: 6 September 2023

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1

Deszcz, Ryszard, Małgorzata Głogowska, Miroslava Petrovic-Torgasev, and Leopold Verstraelen. "Curvature properties of some class of minimal hypersurfaces in Euclidean spaces." Filomat 29, no. 3 (2015): 479–92. http://dx.doi.org/10.2298/fil1503479d.

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We determine curvature properties of pseudosymmetry type of some class of minimal 2-quasiumbilical hypersurfaces in Euclidean spaces En+1, n ? 4. We present examples of such hypersurfaces. The obtained results are used to determine curvature properties of biharmonic hypersurfaces with three distinct principal curvatures in E5. Those hypersurfaces were recently investigated by Y. Fu in [38].

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2

Maheshkumar Kankarej, Manisha. "Different Types of Curvature and Their Vanishing Conditions." Academic Journal of Applied Mathematical Sciences, no. 73 (May 2, 2021): 143–48. http://dx.doi.org/10.32861/ajams.73.143.148.

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In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.

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3

Balkan, Y. S., and N. Aktan. "Almost Kenmotsu $f$-manifolds." Carpathian Mathematical Publications 7, no. 1 (July 6, 2015): 6–21. http://dx.doi.org/10.15330/cmp.7.1.6-21.

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In this paper, we consider a generalization of almost Kenmotsu f-manifolds. We get basic Riemannian curvature, sectional curvatures and scalar curvature properties such type manifolds. Finally, we give two examples to clarify some our results.

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4

Decu, Simona, Stefan Haesen, Leopold Verstraelen, and Gabriel-Eduard Vîlcu. "Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature." Entropy 20, no. 7 (July 14, 2018): 529. http://dx.doi.org/10.3390/e20070529.

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In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=−h∗, i.e., the submanifold is totally geodesic with respect to the Levi–Civita connection.

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5

Peyghan, Esmaeil, and Esa Sharahi. "Vector Bundles and Paracontact Finsler Structures." Facta Universitatis, Series: Mathematics and Informatics 33, no. 2 (September 7, 2018): 231. http://dx.doi.org/10.22190/fumi1802231p.

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Almost paracontact and normal almost paracontact Finsler structures on a vector bundle are defined. Finding some conditions, integrability of these structures are studied. Moreover, we define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find the vertical and horizontal flag curvatures. Then, defining vertical φ-flag curvature, we prove that every locally symmetric para-Sasakian Finsler structure has negative vertical φ-flag curvature. Finally, we define the horizontal and vertical Ricci tensors of a para-Sasakian Finsler structure and study some curvature properties of them.

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6

Blaga, Adara M., and Antonella Nannicini. "On curvature tensors of Norden and metallic pseudo-Riemannian manifolds." Complex Manifolds 6, no. 1 (January 1, 2019): 150–59. http://dx.doi.org/10.1515/coma-2019-0008.

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AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n.

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7

Wang, Bin, Wenzhe Cai, and Qingxuan Shi. "Simplified Data-Driven Model for the Moment Curvature of T-Shaped RC Shear Walls." Advances in Civil Engineering 2019 (November 3, 2019): 1–16. http://dx.doi.org/10.1155/2019/9897827.

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Sectional deformation quantities, such as curvature and ductility, are of prime significance in the displacement-based seismic design and performance evaluation of structural members. However, few studies on the estimates of curvatures at different limit states have been performed on asymmetric flanged walls. In this paper, a parametric study was performed for a series of T-shaped wall cross-sections based on moment-curvature analyses. By investigating the effects of the axial load ratio, reinforcement content, material properties, and geometric parameters on curvatures at the yield and ultimate limit state, we interpret the variation in curvature with different influencing factors in detail according to the changes of the neutral axis depth. Based on the regression analyses of the numerical results of 4941 T-shaped cross-sections, simple expressions to estimate the yield curvature and ultimate curvature for asymmetric flanged walls are developed, and simplified estimates of the ductility capacity including curvature ductility and displacement ductility are further deduced. By comparing with the experimental results, we verify the accuracy of the proposed formulas. Such simple expressions will be valuable for the determination of the displacement response of asymmetric flanged reinforced concrete walls.

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8

Duan, Jun-Sheng. "Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals." Discrete Dynamics in Nature and Society 2019 (December 20, 2019): 1–6. http://dx.doi.org/10.1155/2019/3149602.

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We investigated the golden rectangle and the related Fibonacci spiral and golden spiral. The coordinates of the shrinkage points of a golden rectangle were derived. Properties of shrinkage points were discussed. Based on these properties, we conduct a comparison study for the Fibonacci spiral and golden spiral. Their similarities and differences were looked into by examining their polar coordinate equations, polar radii, arm-radius angles, and curvatures. The golden spiral has constant arm-radius angle and continuous curvature, while the Fibonacci spiral has cyclic varying arm-radius angle and discontinuous curvature.

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9

Sawicz, Katarzyna. "Curvature properties of some class of hypersurfaces in Euclidean spaces." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 165–77. http://dx.doi.org/10.2298/pim141025008s.

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We determine curvature properties of pseudosymmetry type of hypersurfaces in Euclidean spaces En+1, n ? 5, having three distinct nonzero principal curvatures ?1, ?2 and ?3 of multiplicity 1, p and n-p-1, respectively. For some hypersurfaces having this property the sum of ?1, ?2 and ?3 is equal to the trace of the shape operator of M. We present an example of such hypersurface.

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10

Davidov, Johann, and Oleg Mushkarov. "Curvature Properties of Twistor Spaces." Proceedings of the Steklov Institute of Mathematics 311, no. 1 (December 2020): 78–97. http://dx.doi.org/10.1134/s008154382006005x.

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11

Deszcz, Ryszard, and Sahnur Yaprak. "Curvature properties of Cartan hypersurfaces." Colloquium Mathematicum 67, no. 1 (1994): 91–98. http://dx.doi.org/10.4064/cm-67-1-91-98.

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12

Deszcz, Ryszard, Marian Hotloś, Jan Jełowicki, Haradhan Kundu, and Absos Ali Shaikh. "Curvature properties of Gödel metric." International Journal of Geometric Methods in Modern Physics 16, no. 04 (April 2019): 1992002. http://dx.doi.org/10.1142/s0219887819920026.

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13

Shaikh, Absos Ali, Akram Ali, Ali H. Alkhaldi, and Dhyanesh Chakraborty. "Curvature properties of Nariai spacetimes." International Journal of Geometric Methods in Modern Physics 17, no. 03 (February 13, 2020): 2050034. http://dx.doi.org/10.1142/s0219887820500346.

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This paper is concerned with the study of the geometry of (charged) Nariai spacetime, a topological product spacetime, by means of covariant derivative(s) of its various curvature tensors. It is found that on this spacetime the condition [Formula: see text] is satisfied and it also admits the pseudosymmetric type curvature conditions [Formula: see text] and [Formula: see text]. Moreover, it is 4-dimensional Roter type, [Formula: see text]-quasi-Einstein and generalized quasi-Einstein spacetime. The energy–momentum tensor is expressed explicitly by some 1-forms. It is worthy to see that a generalization of such topological product spacetime proposes to exist with a class of generalized recurrent type manifolds which is semisymmetric. It is observed that the rank of [Formula: see text], [Formula: see text], of Nariai spacetime (NS) is 0 whereas in case of charged Nariai spacetime (CNS) it is 2, which exhibits that effects of charge increase the rank of Ricci tensor. Also, due to the presence of charge in CNS, it gives rise to the proper pseudosymmetric type geometric structures.

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14

Atçeken, Mehmet. "Some Curvature Properties of -Manifolds." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/380657.

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15

Gilkey, Peter, Stana Nikčević, and Udo Simon. "Curvature Properties of Weyl Geometries." Results in Mathematics 59, no. 3-4 (April 2, 2011): 523–44. http://dx.doi.org/10.1007/s00025-011-0111-3.

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16

Deszcz, Ryszard, Marian Hotloś, Jan Jełowicki, Haradhan Kundu, and Absos Ali Shaikh. "Curvature properties of Gödel metric." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450025. http://dx.doi.org/10.1142/s021988781450025x.

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The main aim of this paper is to investigate the geometric structures admitting by the Gödel spacetime which produces a new class of semi-Riemannian manifolds. We also consider some extension of Gödel metric.

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17

Koc, Władysław, and Katarzyna Palikowska. "Modelling of joining route segments of different curvature." Baltic Journal of Road and Bridge Engineering 11, no. 1 (March 25, 2016): 1–10. http://dx.doi.org/10.3846/bjrbe.2016.01.

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The paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model. The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves.

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18

Peyghan, E., A. Tayebi, and L. Nourmohammadi Far. "On Twisted Products Finsler Manifolds." ISRN Geometry 2013 (July 10, 2013): 1–12. http://dx.doi.org/10.1155/2013/732432.

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On the product of two Finsler manifolds , we consider the twisted metric which is constructed by using Finsler metrics and on the manifolds and , respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study C-reducible and semi-C-reducible properties of this manifold. Then we obtain the Riemannian curvature and some of non-Riemannian curvatures of the twisted product Finsler manifold such as Berwald curvature, mean Berwald curvature, and we find the relations between these objects and their corresponding objects on and . Finally, we study locally dually flat twisted product Finsler manifold.

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19

Tanriöver, Necmettin. "Some properties of Bertrand curves in Lorentzian n-space 𝕃n." International Journal of Geometric Methods in Modern Physics 13, no. 05 (April 21, 2016): 1650064. http://dx.doi.org/10.1142/s021988781650064x.

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In this paper, Bertrand curves in [Formula: see text]-dimensional Lorentz space [Formula: see text] are defined and some of their properties are determined. Various relationships and characterizations are found between higher order curvatures and their derivatives for Bertrand curve pair. In addition, some relationships are obtained between these curves and general helix, harmonic curvature.

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20

Honda, Shinya. "Multi-Objective Optimization of Variable-Stiffness Composites Fabricated by Tailored Fiber Placement Machine." EPI International Journal of Engineering 2, no. 1 (June 27, 2019): 14–18. http://dx.doi.org/10.25042/epi-ije.022019.04.

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A multi-objective optimization method for the laminated composite fabricated by a tailored fiber placement machine that is an application of embroidering machine is presented. The mechanical properties of composite with curvilinear fibers including stiffness, volume fraction, and density are variable depending on curvatures of fibers. The present study first measures the relation between curvatures and mechanical properties. The measured results indicate that the stiffness of composite decreases linearly as the curvature increases. Then, the obtained relation is applied to the multi-objective optimization where the maximum principal strain and magnitude of curvature are employed as objective functions. Obtained Pareto optimum solutions are widely distributed ranging from the solutions with curvilinear fibers to those with straight fibers, and the curvilinear fiber has still advantages over straight fiber even its weakened stiffness.

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21

Sukhanova, Olga, and Олексій Ларін. "Linear dynamic properties in curved laminated glasses." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 1 (December 31, 2021): 44–47. http://dx.doi.org/10.20998/2078-9130.2021.1.230161.

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The study presents the results of linear dynamics of laminated glass panels with different curvatures. This is an actual task in the field of mechanical engineering, aviation, shipbuilding, energy, architecture, etc. Such composites are durable, easy to care for and have a wide range of design options. The aim of the work is to study the influence of the curvature parameter on the frequencies and modes of composites. The paper considers the linear characteristics for laminated glass with polyvinyl butyral interlayer. The article considers behavior of the triplex and the propagation of elastic waves in the linear state. The paper performs calculations using the finite element method in the framework of modal analysis in a three-dimensional formulation in the framework of a physical linear-elastic formulation. The study uses hexagonal finite element with 8 nodes with 3 degrees of freedom in each. This work model laminated glass with a curvature parameter ranging from 0 mm to 250 mm. The composite consisted of three layers: two glass layers thickness of each was 3 mm, and a polyvinyl butyral interlayer with 0.38 mm thickness. The size of the plates was 500×500 mm. As a boundary condition, the laminate was fixed on two opposite sides. The article performs mesh size convergence analysis. The results of natural frequencies in accordance with the curvature parameter are derived. The graphs of natural vibration modes are also shown, that give a clear view about the state of composites.

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22

Lemesle, Julie, Frederic Robache, Gaetan Le Goic, Alamin Mansouri, Christopher A. Brown, and Maxence Bigerelle. "Surface Reflectance: An Optical Method for Multiscale Curvature Characterization of Wear on Ceramic–Metal Composites." Materials 13, no. 5 (February 25, 2020): 1024. http://dx.doi.org/10.3390/ma13051024.

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Surface gradient characterization by light reflectance (SGCLR) is used for the first time for multiscale curvature calculations and discrimination of worn surfaces on six damaged ceramic–metal composites. Measurements are made using reflectance transformation imaging (RTI). Slope and curvature maps, generated from RTI, are analyzed instead of heights. From multiscale decompositions, bootstrapping, and analysis of variance (ANOVA), a strong correlation (R² = 0.90) is found between the density of furrows of Mehlum curvatures, with a band pass filter at 5.4 µm, present in ceramic grains and their mechanical properties. A strong correlation is found between the mean curvatures of the metal and the ceramics, with a high pass filter at 1286 µm.

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23

Sari, Ramazan. "Some Properties Curvture of Lorentzian Kenmotsu Manifolds." Applied Mathematics and Nonlinear Sciences 5, no. 1 (March 31, 2020): 283–92. http://dx.doi.org/10.2478/amns.2020.1.00026.

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AbstractIn this paper different curvature tensors on Lorentzian Kenmotsu manifod are studied. We investigate constant ϕ–holomorphic sectional curvature and ℒ-sectional curvature of Lorentzian Kenmotsu manifolds, obtaining conditions for them to be constant of Lorentzian Kenmotsu manifolds in such condition. We calculate the Ricci tensor and scalar curvature for all the cases. Moreover we investigate some properties of semi invariant submanifolds of a Lorentzian Kenmotsu space form. We show that if a semi-invariant submanifold of a Lorentzian Kenmotsu space form M is totally geodesic, then M is an η−Einstein manifold. We consider sectional curvature of semi invariant product of a Lorentzian Kenmotsu manifolds.

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24

Azarhooshang, Nazanin, Prithviraj Sengupta, and Bhaskar DasGupta. "A Review of and Some Results for Ollivier–Ricci Network Curvature." Mathematics 8, no. 9 (August 24, 2020): 1416. http://dx.doi.org/10.3390/math8091416.

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Characterizing topological properties and anomalous behaviors of higher-dimensional topological spaces via notions of curvatures is by now quite common in mainstream physics and mathematics, and it is therefore natural to try to extend these notions from the non-network domains in a suitable way to the network science domain. In this article we discuss one such extension, namely Ollivier’s discretization of Ricci curvature. We first motivate, define and illustrate the Ollivier–Ricci Curvature. In the next section we provide some “not-previously-published” bounds on the exact and approximate computation of the curvature measure. In the penultimate section we review a method based on the linear sketching technique for efficient approximate computation of the Ollivier–Ricci network curvature. Finally in the last section we provide concluding remarks with pointers for further reading.

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25

Ross, Nicholas M., Alexander Goettker, Alexander C. Schütz, Doris I. Braun, and Karl R. Gegenfurtner. "Discrimination of curvature from motion during smooth pursuit eye movements and fixation." Journal of Neurophysiology 118, no. 3 (September 1, 2017): 1762–74. http://dx.doi.org/10.1152/jn.00324.2017.

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Smooth pursuit and motion perception have mainly been investigated with stimuli moving along linear trajectories. Here we studied the quality of pursuit movements to curved motion trajectories in human observers and examined whether the pursuit responses would be sensitive enough to discriminate various degrees of curvature. In a two-interval forced-choice task subjects pursued a Gaussian blob moving along a curved trajectory and then indicated in which interval the curve was flatter. We also measured discrimination thresholds for the same curvatures during fixation. Motion curvature had some specific effects on smooth pursuit properties: trajectories with larger amounts of curvature elicited lower open-loop acceleration, lower pursuit gain, and larger catch-up saccades compared with less curved trajectories. Initially, target motion curvatures were underestimated; however, ∼300 ms after pursuit onset pursuit responses closely matched the actual curved trajectory. We calculated perceptual thresholds for curvature discrimination, which were on the order of 1.5 degrees of visual angle (°) for a 7.9° curvature standard. Oculometric sensitivity to curvature discrimination based on the whole pursuit trajectory was quite similar to perceptual performance. Oculometric thresholds based on smaller time windows were higher. Thus smooth pursuit can quite accurately follow moving targets with curved trajectories, but temporal integration over longer periods is necessary to reach perceptual thresholds for curvature discrimination. NEW & NOTEWORTHY Even though motion trajectories in the real world are frequently curved, most studies of smooth pursuit and motion perception have investigated linear motion. We show that pursuit initially underestimates the curvature of target motion and is able to reproduce the target curvature ∼300 ms after pursuit onset. Temporal integration of target motion over longer periods is necessary for pursuit to reach the level of precision found in perceptual discrimination of curvature.

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26

Lee, Tae-Hyun, Kyung-Il Joo, and Hak-Rin Kim. "Switchable Lens Design for Multi-View 2D/3D Switching Display with Wide-Viewing Window." Crystals 10, no. 5 (May 24, 2020): 418. http://dx.doi.org/10.3390/cryst10050418.

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We improved the three-dimensional (3D) crosstalk level of multi-view 3D displays using a lens array with small f-number, thereby facilitating a wide 3D viewing window. In particular, we designed a polarization-dependent-switching liquid crystal (LC)-based gradient refractive index (GRIN) lens array that could be switched between 2D and 3D viewing modes. For the GRIN lens with a small f-number (1.08), we studied the effect of the interfacial curvature between the plano-concave isotropic polymer layer and the plano-convex birefringent LC layer on the aberration properties. We examined the conventional spherical, quadratic polynomial aspherical, and a high-order (fourth-order) polynomial aspherical curvature. For the high-order polynomial aspherical curvature, the achievable transverse spherical aberration (TSA = 10.2 µm) was considerably lower than that with the spherical (TSA = 100.3 µm) and quadratic polynomial aspherical (TSA = 30.4 µm) curvatures. Consequently, the angular luminance distributions for each view were sharper for the high-order polynomial interfacial curvature. We designed multi-view (43-view) 3D displays using the arrays of switchable LC lenses with different curvatures, and the average adjacent crosstalk levels within the entire viewing window (50°) were 68.5%, 73.3%, and 60.0% for the spherical, quadratic polynomial aspherical, and high-order polynomial aspherical curvatures, respectively.

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27

Shichang, Shu, and Liu Sanyang. "The curvature and topological properties of hypersurfaces with constant scalar curvature." Bulletin of the Australian Mathematical Society 70, no. 1 (August 2004): 35–44. http://dx.doi.org/10.1017/s0004972700035796.

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In this paper, we consider n (n ≥ 3)-dimensional compact oriented connected hypersurfaces with constant scalar curvature n(n − 1)r in the unit sphere Sn+1(1). We prove that, if r ≥ (n − 2)/(n − 1) and S ≤ (n − 1)(n(r − 1) + 2)/(n − 2) + (n − 2)/(n(r − 1) + 2), then either M is diffeomorphic to a spherical space form if n = 3; or M is homeomorphic to a sphere if n ≥ 4; or M is isometric to the Riemannian product , where c2 = (n − 2)/(nr) and S is the squared norm of the second fundamental form of M.

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28

MASOTTI, DANIELE, ELISA FICARRA, ENRICO MACII, and LUCA BENINI. "OPTIMIZED TECHNIQUE FOR DNA STRUCTURAL PROPERTIES DISCOVERING." International Journal on Artificial Intelligence Tools 15, no. 05 (October 2006): 695–709. http://dx.doi.org/10.1142/s0218213006002886.

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An automated algorithm is presented to determine the DNA molecule intrinsic curvature profiles and the molecular spatial orientations in Atomic Force Microscope images. The curvature is composed by static and dynamic contributions. The former is the intrinsic curvature, a function of the DNA nucleotide sequence, while the latter is due to thermal fluctuations. This algorithm allows to reconstruct the intrinsic curvature profile excluding the thermal contribution. The DNA intrinsic curvature profile is computed in consequence of the detection of the correct spatial orientation of the molecules on the AFM substrate following the DNA deposition process. To discover the correct molecular orientations, we propose a fast heuristic orientation finding algorithm, that modifies one DNA molecular orientation at a time with linear-time heuristic transitions.

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29

RAFIE-RAD, M. "ON THE RIEMANN CURVATURE OPERATORS IN RANDERS SPACES." International Journal of Geometric Methods in Modern Physics 10, no. 09 (August 30, 2013): 1350044. http://dx.doi.org/10.1142/s0219887813500448.

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The Riemann curvature in Riemann–Finsler geometry can be regarded as a collection of linear operators on the tangent spaces. The algebraic properties of these operators may be linked to the geometry and the topology of the underlying space. The principal curvatures of a Finsler space (M, F) at a point x are the eigenvalues of the Riemann curvature operator at x. They are real functions κ on the slit tangent manifold TM0. A principal curvature κ(x, y) is said to be isotropic (respectively, quadratic) if κ(x, y)/F(x, y) is a function of x only (respectively, κ(x, y) is quadratic with respect to y). On the other hand, the Randers metrics are the most popular and prominent metrics in pure and applied disciplines. Here, it is proved that if a Randers metric admits an isotropic principal curvature, then F is of isotropic S-curvature. The same result is also established for F to admit a quadratic principal curvature. These results extend Shen's verbal results about Randers metrics of scalar flag curvature K = K(x) as well as those Randers metrics with quadratic Riemann curvature operator. The Riemann curvature [Formula: see text] may be broken into two operators [Formula: see text] and [Formula: see text]. The isotropic and quadratic principal curvature are characterized in terms of the eigenvalues of [Formula: see text] and [Formula: see text].

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30

Wu, Jiunn-Jong. "The Properties of Asperities of Real Surfaces." Journal of Tribology 123, no. 4 (December 8, 2000): 872–83. http://dx.doi.org/10.1115/1.1353179.

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The properties of asperities are investigated. It is found that the asperity size distribution of asperities can be estimated by the auto-correlation function. New definitions for asperity and asperity curvature are employed. It is found that asperity curvature can be estimated by root mean square curvature of profile. With the finding of this paper, the statistical contact model can be used more accurately.

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31

Zamfirescu, Tudor. "Curvature properties of typical convex surfaces." Pacific Journal of Mathematics 131, no. 1 (January 1, 1988): 191–207. http://dx.doi.org/10.2140/pjm.1988.131.191.

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32

Chuaqui, Martin, Peter Duren, and Brad Osgood. "Curvature Properties of Planar Harmonic Mappings." Computational Methods and Function Theory 4, no. 1 (August 2004): 127–42. http://dx.doi.org/10.1007/bf03321060.

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33

Sheng, Weimin, and Lisheng Wang. "Variational properties of quadratic curvature functionals." Science China Mathematics 62, no. 9 (June 15, 2018): 1765–78. http://dx.doi.org/10.1007/s11425-017-9232-6.

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34

Shaikh, Absos Ali, Akram Ali, Ali H. Alkhaldi, and Dhyanesh Chakraborty. "Curvature properties of Melvin magnetic metric." Journal of Geometry and Physics 150 (April 2020): 103593. http://dx.doi.org/10.1016/j.geomphys.2019.103593.

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35

Shaikh, Absos Ali, and Dhyanesh Chakraborty. "Curvature properties of Kantowski–Sachs metric." Journal of Geometry and Physics 160 (February 2021): 103970. http://dx.doi.org/10.1016/j.geomphys.2020.103970.

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36

Chen, Xinyue, and Zhongmin Shen. "Finsler metrics with special curvature properties." Periodica Mathematica Hungarica 48, no. 1/2 (2004): 33–47. http://dx.doi.org/10.1023/b:mahu.0000038964.96496.32.

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37

Deszcz, Ryszard, and Sahnur Yaprak. "Curvature properties of certain pseudosymmetric manifolds." Publicationes Mathematicae Debrecen 45, no. 3-4 (October 1, 1994): 333–45. http://dx.doi.org/10.5486/pmd.1994.1451.

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38

Taleshian, A., and A. A. Hosseinzadeh. "Some Curvature Properties of Kenmotsu Manifolds." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 85, no. 3 (July 14, 2015): 407–13. http://dx.doi.org/10.1007/s40010-015-0215-3.

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Sun, Lingen, Xiaoling Zhang, and Mengke Wu. "Finsler Warped Product Metrics with Special Curvature Properties." Axioms 12, no. 8 (August 12, 2023): 784. http://dx.doi.org/10.3390/axioms12080784.

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The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing χ-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the χ-curvature vanishes if and only if the H-curvature vanishes.

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HERTEL, RICCARDO. "CURVATURE-INDUCED MAGNETOCHIRALITY." SPIN 03, no. 03 (September 2013): 1340009. http://dx.doi.org/10.1142/s2010324713400092.

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Curved geometries like nanotubes and flexible membranes generally differ from flat films by internal strain, geodesic pathways for transport phenomena, and a break of the local inversion symmetry. In ferromagnetism, these characteristics can lead to surprising effects, especially when the curvature radius reaches intrinsic length scales, like the domain wall width or the magnon wave length. Simulation studies demonstrate that curved ferromagnetic thin films display magnetochiral properties similar to the Dzyaloshinskii–Moriya interaction (DMI). In close analogy to the emerging field of flexoelectricity, it is suggested that the controlled bending of ferromagnetic membranes provides a new, reversible and universal method to manipulate their magnetic properties.

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Feng, Tao, Lishi Wang, Zhongmin Tang, Shanwen Yu, Zhixiang Bu, Xinbin Hu, and Yihang Cheng. "Effect of Trajectory Curvature on the Microstructure and Properties of Surfacing Wall Formed with the Process of Wire Arc Additive Manufacturing." Coatings 9, no. 12 (December 11, 2019): 848. http://dx.doi.org/10.3390/coatings9120848.

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Curvature effects are typically present in the process of additive manufacturing (AM), particularly for wire arc additive manufacturing. In this paper, stainless-steel wire was adopted to deposit thin-walled samples with different curvatures. Optical microscopy, SEM, EDS and micro-hardness was used to analyse the microstructure, composition and properties of the samples. The result shows that the bottom region of the thin-walled sample had a mainly planar and cellular crystal microstructure. For the middle region, the microstructure revealed mainly dendrites, and the top layer has equiaxed dendrite morphology. The microhardness value of the bottom was greater than that of the middle, and the microhardness value of the middle was greater than that of the top. Moreover, the grain size of the inner part (direct to curvature radius) was larger than that of the outer part, and the micro-hardness value exhibited an increasing tendency from the inner to the outer side. With enlarging curvature, the degree of grain size differences and micro-hardness variants decreased. Finally, an investigation with a low carbon steel wire showed that it had a similar curvature effect for its AM specimen.

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Sebekovic, Aleksandar, Miroslava Petrovic-Torgasev, and Anica Pantic. "Pseudosymmetry properties of generalised Wintgen ideal Legendrian submanifolds." Filomat 33, no. 4 (2019): 1209–15. http://dx.doi.org/10.2298/fil1904209s.

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For Legendrian submanifolds Mn in Sasakian space forms ?M2n+1(c), I. Mihai obtained an inequality relating the normalised scalar curvature (intrinsic invariant) and the squared mean curvature and the normalised scalar normal curvature of M in the ambient space ?M (extrinsic invariants) which is called the generalised Wintgen inequality, characterising also the corresponding equality case. And a Legendrian submanifold Mn in Sasakian space forms ?M2n+1(c) is said to be generalised Wintgen ideal Legendrian submanifold of ?M2n+1(c) when it realises at everyone of its points the equality in such inequality. Characterisations based on some basic intrinsic symmetries involving the Riemann-Cristoffel curvature tensor, the Ricci tensor and the Weyl conformal curvature tensor belonging to the class of pseudosymmetries in the sense of Deszcz of such generalised Wintgen ideal Legendrian submanifolds are given.

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Koler, Cheryl Akner, and Lars Bergström. "Complex Curvatures in Form Theory and String Theory." Leonardo 38, no. 3 (June 2005): 226–31. http://dx.doi.org/10.1162/0024094054028985.

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The authors use new aesthetic criteria concerning structures and properties to explain parallel concepts within theoretical astroparticle physics and contemporary form/compositional research. These aesthetic criteria stem from complex curvature models developed both in string theory and in artistic perceptual research on transitional surfaces and concavities. The authors compare the complex curvatures of the mathematically derived Calabi-Yau manifold with one of Akner Koler's sculptures, which explores an organic interpretation of the looping curvature of a Möbius strip. A goal of the collaboration is to gain experience and insight into the twisting paradoxical forces in the 3D world and to explore the properties of transparency as applied to the Calabi-Yau manifold and a point cloud translation of Akner Koler's sculpture.

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Shah, Riddhi Jung. "Some Curvature Properties of D-conformal Curvature Tensor on LP-Sasakian Manifolds." Journal of Institute of Science and Technology 19, no. 1 (November 8, 2015): 30–34. http://dx.doi.org/10.3126/jist.v19i1.13823.

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This paper deals with the study of geometry of Lorentzian para-Sasakian manifolds. We investigate some properties of D-conformally flat, D-conformally semi-symmetric, Xi-D-conformally flat and Phi-D-conformally flat curvature conditions on Lorentzian para-Sasakian manifolds. Also it is proved that in each curvature condition an LP-Sasakian manifold (Mn,g)(n>3) is an eta-Einstein manifold.Journal of Institute of Science and Technology, 2014, 19(1): 30-34

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Najafi, B., Z. Shen, and A. Tayebi. "Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties." Geometriae Dedicata 131, no. 1 (December 29, 2007): 87–97. http://dx.doi.org/10.1007/s10711-007-9218-9.

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Mandal, Krishanu, and Uday Chand De. "Some curvature properties of paracontact metric manifolds." Advances in Pure and Applied Mathematics 9, no. 3 (July 1, 2018): 159–65. http://dx.doi.org/10.1515/apam-2017-0064.

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AbstractThe purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying{\nabla_{\xi}h=0}and such that the sectional curvature of the plane section containing ξ equals a non-zero constantc. Also, we study paracontact metric manifolds satisfying the curvature condition{Q\cdot R=0}, whereQandRare the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed.

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Liu, Rong, Jundong Liu, Terence T. Lao, Michael Ying, and Xinbo Wu. "Determination of leg cross-sectional curvatures and application in pressure prediction for lower body compression garments." Textile Research Journal 89, no. 10 (June 11, 2018): 1835–52. http://dx.doi.org/10.1177/0040517518779246.

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It has been recognized that the cross-sectional curvatures of lower extremities directly influence pressure magnitudes and distributions exerted by compression garments. In the practice of compression therapy, higher peak pressures produced by compression shells occurred at anatomic sites with smaller radius of curvatures and led to side effects and discomfort perception. An effective and operational method to determine leg curvature properties in order to predict pressure performances is desirable to improve comfort and mechanical function of compression garment. By employing three-dimensional (3D) digital anthropometry and two-dimensional (2D) digital image simulation, the curvatures and radius of curvatures of a total of 300 cross-sectional slices involving 1200 anatomic sites along the lower limbs were determined onto the ten healthy female subjects when they were and were not wearing compression stockings. Based on the determined cross-sectional characteristics, the skin pressures were calculated using the circumference-based and the radius of curvature-based Laplace’s equations, respectively, which were further validated against the experimental skin pressures measured by a PicoPress transducer. This study provided quantitative evidence in the exploration of the working mechanisms of uneven pressures produced by compression garments, and established a standardized method to determine cross-section-related curvature characteristics for pressure assessment and prediction, which will contribute to improving user compliance of compression garments in long-term wear.

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CAPPELLETTI-MONTANO, BENIAMINO, ANTONIO DE NICOLA, and IVAN YUDIN. "CURVATURE PROPERTIES OF 3-QUASI-SASAKIAN MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 08 (August 7, 2013): 1360008. http://dx.doi.org/10.1142/s0219887813600086.

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We find some curvature properties of 3-quasi-Sasakian manifolds which extend certain well-known identities holding in the Sasakian case. As an application, we prove that any 3-quasi-Sasakian manifold of constant horizontal sectional curvature is necessarily either 3-α-Sasakian or 3-cosymplectic.

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Arava, Clement Manohar, Sanjib Nayak, Kwok Sum Chan, and Vellaisamy A. L. Roy. "A study on the electronic properties of A site and B site doped SrTiO₃ for thermoelectric applications using first-principles calculations." Physica Scripta 97, no. 3 (February 16, 2022): 035808. http://dx.doi.org/10.1088/1402-4896/ac518e.

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Abstract In SrTiO3, the nature of dopants and their substitution at the A or B site becomes a critical factor in determining the electrical conductivity, Seebeck coefficient, and thermal conductivity. The electronic band structure and the density of states (DOS) for the ab-initio study using different dopants were estimated using PBE-GGA approximation. The size, site of substitution, and nature of dopants cause significant changes in the lattice dimensions, band structure, band curvatures, and the density of states, which reflect as changes in the effective mass m B i ⁎ . The effective mass m B i ⁎ is calculated from the curvature of the bottom-most conduction band using the one-band effective mass approximation. Pentavalent substitutions on the B site of SrTiO3 affect the conduction band’s curvature differently than with trivalent substitutions on the A site. They also exhibit an opposite trend in the change in band curvature according to the dopant’s ionic radius. In contrast, isovalent dopants showed no change in the band curvature except for the bandgap modification. In this paper, we have provided a semi-quantitative understanding regarding the thermoelectric properties like conductivity and Seebeck coefficient that get affected due to the substituent’s nature and site at which it substitutes.

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Deszcz, Ryszard, Małgorzata Głogowska, Jan Jełowicki, and Georges Zafindratafa. "Curvature properties of some class of warped product manifolds." International Journal of Geometric Methods in Modern Physics 13, no. 01 (January 2016): 1550135. http://dx.doi.org/10.1142/s0219887815501352.

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We prove that warped product manifolds with [Formula: see text]-dimensional base, [Formula: see text] satisfy some pseudosymmetry type curvature conditions. These conditions are formed from the metric tensor [Formula: see text], the Riemann–Christoffel curvature tensor [Formula: see text], the Ricci tensor [Formula: see text] and the Weyl conformal curvature [Formula: see text] of the considered manifolds. The main result of the paper states that if [Formula: see text] and the fiber is a semi-Riemannian space of constant curvature (when [Formula: see text] is greater or equal to 5) then the [Formula: see text]-tensors [Formula: see text] and [Formula: see text] of such warped products are proportional to the [Formula: see text]-tensor [Formula: see text] and the tensor [Formula: see text] is a linear combination of some Kulkarni–Nomizu products formed from the tensors [Formula: see text] and [Formula: see text]. We also obtain curvature properties of this kind of quasi-Einstein and 2-quasi-Einstein manifolds, and in particular, of the Goedel metric, generalized spherically symmetric metrics and generalized Vaidya metrics.

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