Статті в журналах: "Spacelink"

1

La Russa, Carol J. "NASA Spacelink [Information system]." Government Publications Review 18, no. 2 (March 1991): 198. http://dx.doi.org/10.1016/0277-9390(91)90070-e.

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2

La Russa, Carol J. "NASA Spacelink user's guide." Government Publications Review 18, no. 2 (March 1991): 198–99. http://dx.doi.org/10.1016/0277-9390(91)90071-5.

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3

Schack, Markham B. "Exploring Science with NASA Spacelink." Science Activities: Classroom Projects and Curriculum Ideas 32, no. 1 (March 1995): 8–10. http://dx.doi.org/10.1080/00368121.1995.10113167.

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4

Rootes, John, and Diane Flynn. "European Space-Technology Transfer Support for SMEs." Industry and Higher Education 15, no. 1 (February 2001): 74–78. http://dx.doi.org/10.5367/000000001101295399.

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Since the inception of the European Space Agency's (ESA) technology transfer programme (TTP) in 1990, more than 400 potential spin-off technologies have been marketed throughout Europe by the Spacelink network of technology brokers that have been contracted to assist ESA in implementing the programme. During the eight years of programme operation, more than 70 transfers of space technology to many sectors of industry throughout Europe have been achieved. Over half of the technology donor and receiver companies to date have been SMEs. The work done by the TTP and Spacelink is complemented by ESA's recently established SME Initiative, which aims to promote better interactions between SMEs and the space industry as a whole. This paper describes both of these ESA programmes, and outlines ways in which SMEs can be supported and participate in space technology transfer activities.

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5

Bronson, Roberta J. "SPACELINE: The Final Frontier?" Medical Reference Services Quarterly 16, no. 1 (February 27, 1997): 39–46. http://dx.doi.org/10.1300/j115v16n01_04.

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6

Snodgrass, Susan. "Karen Reimer: Shoretime Spaceline." TEXTILE 15, no. 3 (March 27, 2017): 324–31. http://dx.doi.org/10.1080/14759756.2017.1299321.

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7

Mason, D. P., and M. Tsamparlis. "Spacelike conformal Killing vectors and spacelike congruences." Journal of Mathematical Physics 26, no. 11 (November 1985): 2881–901. http://dx.doi.org/10.1063/1.526714.

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8

Kumar, Santosh, and Buddhadev Pal. "K-type slant helices on spacelike and timelike surfaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 25, no. 2 (November 17, 2021): 201–20. http://dx.doi.org/10.12697/acutm.2021.25.14.

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We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E13, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.

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9

Cuong, Dang Van. "The bi-normal fields on spacelike surfaces in ℝ14". Asian-European Journal of Mathematics 09, № 03 (2 серпня 2016): 1650052. http://dx.doi.org/10.1142/s1793557116500522.

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A normal field [Formula: see text] on a spacelike surface in [Formula: see text] is called bi-normal if [Formula: see text], the determinant of the Weingarten map associated to [Formula: see text], is zero. In this paper, we give a criterion to check if a normal field is bi-normal. Then we study the relationship between the spacelike pseudo-planar surfaces and spacelike pseudo-umbilical surfaces. We also study the bi-normal fields on spacelike ruled surfaces and spacelike surfaces of revolution.

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10

ARNTZENIUS, FRANK. "Spacelike Connections." British Journal for the Philosophy of Science 45, no. 1 (March 1, 1994): 201–17. http://dx.doi.org/10.1093/bjps/45.1.201.

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11

Gutperle, Michael, and Andrew Strominger. "Spacelike branes." Journal of High Energy Physics 2002, no. 04 (April 11, 2002): 018. http://dx.doi.org/10.1088/1126-6708/2002/04/018.

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12

CABALLERO, MAGDALENA, ALFONSO ROMERO, and RAFAEL M. RUBIO. "COMPLETE CMC SPACELIKE SURFACES WITH BOUNDED HYPERBOLIC ANGLE IN GENERALIZED ROBERTSON–WALKER SPACETIMES." International Journal of Geometric Methods in Modern Physics 07, no. 06 (September 2010): 961–78. http://dx.doi.org/10.1142/s0219887810004658.

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Complete spacelike surfaces with constant mean curvature (CMC) and bounded hyperbolic angle in Generalized Robertson–Walker (GRW) spacetimes, obeying certain natural curvature assumptions, are studied. This boundedness assumption arises as a natural extension of the notion of bounded hyperbolic image of a spacelike surface in the 3-dimensional Lorentz–Minkowski spacetime. The results obtained apply to complete CMC spacelike surfaces lying between two spacelike slices in an GRW spacetime, in the steady state spacetime and in a static GRW spacetime. As an application, uniqueness and non-existence theorems for certain CMC spacelike surface differential equations in a wide family of open GRW spacetimes are given.

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13

Kusak Samanci, Hatce, and Ayhan Yildiz. "The slant helices according to N-Bishop frame of the spacelike curve with spacelike principal normal in Minkowski 3-space." Asian-European Journal of Mathematics 12, no. 06 (October 14, 2019): 2040009. http://dx.doi.org/10.1142/s1793557120400094.

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If the principal normal vector field of a curve makes a constant angle with constant direction, this curve is called as slant helix. In this paper, a slant helix is defined according to N-Bishop frame of the spacelike curve with a spacelike principal normal. Some characterizations of the slant helices are obtained according to spacelike curve N-Bishop frame with a spacelike principal normal, benefiting from the definition of the slant helices.

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14

PYO, JUNCHEOL, and KEOMKYO SEO. "SPACELIKE CAPILLARY SURFACES IN THE LORENTZ–MINKOWSKI SPACE." Bulletin of the Australian Mathematical Society 84, no. 3 (August 9, 2011): 362–71. http://dx.doi.org/10.1017/s0004972711002528.

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AbstractFor a compact spacelike constant mean curvature surface with nonempty boundary in the three-dimensional Lorentz–Minkowski space, we introduce a rotation index of the lines of curvature at the boundary umbilical point, which was developed by Choe [‘Sufficient conditions for constant mean curvature surfaces to be round’, Math. Ann.323(1) (2002), 143–156]. Using the concept of the rotation index at the interior and boundary umbilical points and applying the Poincaré–Hopf index formula, we prove that a compact immersed spacelike disk type capillary surface with less than four vertices in a domain of $\Bbb L^3$ bounded by (spacelike or timelike) totally umbilical surfaces is part of a (spacelike) plane or a hyperbolic plane. Moreover, we prove that the only immersed spacelike disk type capillary surface inside a de Sitter surface in $\Bbb L^3$ is part of (spacelike) plane or a hyperbolic plane.

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15

Mert, Tugba, and Baki Karlıga. "Constant angle spacelike surface in de Sitter space S₁³." Boletim da Sociedade Paranaense de Matemática 35, no. 3 (April 30, 2017): 79–93. http://dx.doi.org/10.5269/bspm.v35i3.24398.

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In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

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16

ROMERO, A., R. M. RUBIO, and J. J. SALAMANCA. "PARABOLICITY OF SPACELIKE HYPERSURFACES IN GENERALIZED ROBERTSON–WALKER SPACETIMES: APPLICATIONS TO UNIQUENESS RESULTS." International Journal of Geometric Methods in Modern Physics 10, no. 08 (August 7, 2013): 1360014. http://dx.doi.org/10.1142/s0219887813600141.

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We study non-compact complete spacelike hypersurfaces in generalized Robertson–Walker spacetimes of arbitrary dimension whose fiber is parabolic. Under boundedness assumptions on the warping function restricted on a spacelike hypersurface and on the hyperbolic angle of the hypersurface, we prove that a complete spacelike hypersurface is parabolic if the Riemannian universal covering of the fiber is so. As an application of this new technique, several uniqueness results on complete maximal spacelike hypersurfaces are obtained. Also, the corresponding Calabi–Bernstein problems are solved.

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17

ALEDO, JUAN ÁNGEL, ALFONSO ROMERO, and RAFAEL M. RUBIO. "UPPER AND LOWER BOUNDS FOR THE VOLUME OF A COMPACT SPACELIKE HYPERSURFACE IN A GENERALIZED ROBERTSON–WALKER SPACETIME." International Journal of Geometric Methods in Modern Physics 11, no. 01 (December 16, 2013): 1450006. http://dx.doi.org/10.1142/s0219887814500066.

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We provide upper and lower bounds for the volume of a compact spacelike hypersurface in an (n + 1)-dimensional Generalized Robertson–Walker (GRW) spacetime in terms of the volume of the fiber, the hyperbolic angle function and the warping function. Under several geometrical and physical assumptions, we characterize the spacelike slices as the only spacelike hypersurfaces where these bounds are attained. As a consequence of these results, we get an upper bound for the first eigenvalue of a compact spacelike surface in a three-dimensional GRW spacetime whose fiber is a topological sphere, which includes the case of the three-dimensional De Sitter spacetime, and show that the bound is attained if and only if M is a spacelike slice.

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18

Gao, Ya, Jing-Hua Li, and Jing Mao. "Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz–Minkowski plane R12." Journal of Mathematical Physics 63, no. 3 (March 1, 2022): 033508. http://dx.doi.org/10.1063/5.0071167.

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In this paper, we investigate the evolution of spacelike curves in the Lorentz–Minkowski plane [Formula: see text] along prescribed geometric flows (including the classical curve shortening flow or mean curvature flow as a special case), which correspond to a class of quasilinear parabolic initial boundary value problems, and can prove that this flow exists for all time. Moreover, we can also show that the evolving spacelike curves converge to a spacelike straight line or a spacelike grim reaper curve as time tends to infinity.

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19

ALÍAS, LUIS J., and A. GERVASIO COLARES. "Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 3 (November 2007): 703–29. http://dx.doi.org/10.1017/s0305004107000576.

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AbstractIn this paper we study the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker (GRW) spacetimes. In particular, we consider the following question: under what conditions must a compact spacelike hypersurface with constant higher order mean curvature in a spatially closed GRW spacetime be a spacelike slice? We prove that this happens, essentially, under the so callednull convergence condition. Our approach is based on the use of the Newton transformations (and their associated differential operators) and the Minkowski formulae for spacelike hypersurfaces.

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20

Körpınar, Talat, and Essin Turhan. "CHARACTERIZATION OF SPACELIKE BIHARMONIC CURVES WITH TIMELIKE BINORMAL ACCORDING TO FLAT METRIC IN LORENTZIAN HEISENBERG GROUP Heis³ - doi: 10.5269/bspm.v30i2.14706." Boletim da Sociedade Paranaense de Matemática 30, no. 2 (September 21, 2011): 101–7. http://dx.doi.org/10.5269/bspm.v30i2.14706.

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In this paper, we study spacelike biharmonic curves with timelike binormal according to flat metric in the Lorentzian Heisenberg group Heis³. We characterize spacelike biharmonic curves with timelike binormal in terms of their curvature and torsion. Additionally, we determine the parametric representation of the spacelike biharmonic curves with timelike binormal according to flat metric from this characterization.

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21

Palomo, Francisco J., and Alfonso Romero. "On spacelike surfaces in four-dimensional Lorentz–Minkowski spacetime through a light cone." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143, no. 4 (July 17, 2013): 881–92. http://dx.doi.org/10.1017/s0308210511001119.

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On any spacelike surface in a light cone of four-dimensional Lorentz–Minkowski space, a distinguished smooth function is considered. We show how both extrinsic and intrinsic geometry of such a surface are codified by this function. The existence of a local maximum is assumed to decide when the spacelike surface must be totally umbilical, deriving a Liebmann-type result. Two remarkable families of examples of spacelike surfaces in a light cone are explicitly constructed. Finally, several results that involve the first eigenvalue of the Laplace operator of a compact spacelike surface in a light cone are obtained.

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22

Li, Pengcheng, and Donghe Pei. "Nullcone Fronts of Spacelike Framed Curves in Minkowski 3-Space." Mathematics 9, no. 22 (November 18, 2021): 2939. http://dx.doi.org/10.3390/math9222939.

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The investigation of objects in Minkowski space is of great significance, especially for those objects with mathematical and physical backgrounds. In this paper, we study nullcone fronts, which are formed by the light rays emitted from points on a spacelike curve. However, if the spacelike curve is singular, then we cannot use the usual tools and methods to study related issues. To solve these problems, we show the definition of spacelike framed curves in Minkowski 3-space, whose original curves may contain singularities. Then, the singularities of the nullcone fronts are characterized by using framed curvatures of spacelike framed curves. Finally, we exhibit some examples to illustrate our results.

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23

Öztürk, Ufuk, Emilija Nesovic, and Öztürk Koç. "On k-type spacelike slant helices lying on lightlike surfaces." Filomat 33, no. 9 (2019): 2781–96. http://dx.doi.org/10.2298/fil1909781o.

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In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E31 according to their Darboux frame for k ? {0,1,2}. We obtain the necessary and the sufficient conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geodesic torsion. Finally, we give some examples.

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24

Li, Yanlin, Maryam T. Aldossary, and Rashad A. Abdel-Baky. "Spacelike Circular Surfaces in Minkowski 3-Space." Symmetry 15, no. 1 (January 6, 2023): 173. http://dx.doi.org/10.3390/sym15010173.

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The approach of the paper is on spacelike circular surfaces in the Minkowski 3-space. A spacelike circular surface is a one-parameter family of Lorentzian circles with a fixed radius regarding a non-null curve, which acts as the spine curve, and it has symmetrical properties. In the study, we have parametrized spacelike circular surfaces and have provided their geometric and singularity properties such as Gaussian and mean curvatures, comparing them with those of ruled surfaces and the classification of singularities. Furthermore, the conditions for spacelike roller coaster surfaces to be flat or minimal surfaces are obtained. Meanwhile, we support the results of the approach with some examples.

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25

Körpınar, Talat, and Essin Turhan. "ON SPACELIKE BIHARMONIC SLANT HELICES ACCORDING TO BISHOP FRAME IN THE LORENTZIAN GROUP OF RIGID MOTIONS E(1,1) - doi: 10.5269/bspm.v30i2.14558." Boletim da Sociedade Paranaense de Matemática 30, no. 2 (September 14, 2011): 91–100. http://dx.doi.org/10.5269/bspm.v30i2.14558.

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Анотація:

In this paper, we study spacelike biharmonic slant helices according to Bishop frame in the Lorentzian group of rigid motions E(1,1). We characterize the spacelike biharmonic slant helices in terms of their curvatures in the Lorentzian group of rigid motions E(1,1). Finally, we obtain parametric equations of spacelike biharmonic slant helices according to Bishop frame in the Lorentzian group of rigid motions E(1,1).

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26

Morinelli, Vincenzo, and Karl-Henning Rehren. "Spacelike deformations: higher-helicity fields from scalar fields." Letters in Mathematical Physics 110, no. 8 (June 11, 2020): 2019–38. http://dx.doi.org/10.1007/s11005-020-01294-w.

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Abstract In contrast to Hamiltonian perturbation theory which changes the time evolution, “spacelike deformations” proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of spacelike deformations of the complex massless Klein–Gordon quantum field into fields of higher helicity. A similar but simpler instance of spacelike deformation allows to increase the mass of scalar fields.

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27

Altınbaş, Hasan, Bülent Altunkaya, and Levent Kula. "Polynomial helices in the n-dimensional semi-Euclidean space with index two." Filomat 34, no. 14 (2020): 4861–72. http://dx.doi.org/10.2298/fil2014861a.

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In this article, we investigate polynomial helices in the n-dimensional semi-Euclidean space with index two for n ? 4. We obtain some families of spacelike and timelike polynomial helices. These helices have spacelike or timelike or null axes. After that, we give some examples of the spacelike and the timelike polynomial helices in the n-dimensional semi-Euclidean space with index two for n = 4,5 and 6.

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28

Bayard, Pierre, та Federico Sánchez-Bringas. "Geometric invariants and principal configurations on spacelike surfaces immersed in ℝ3,1". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, № 6 (грудень 2010): 1141–60. http://dx.doi.org/10.1017/s0308210509001358.

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Анотація:

We describe the numerical invariants and the curvature ellipse attached to the second fundamental form of a spacelike surface in a four-dimensional Minkowski space. We then study the configuration of the V-principal curvature lines on a spacelike surface when the normal field V is lightlike (the lightcone configuration). We end with some observations on the mean directionally curved lines and on the asymptotic lines on spacelike surfaces.

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29

Johnson, R. F., and P. L. Smith. "Future spacelift projection." Space Policy 14, no. 3 (August 1998): 145–51. http://dx.doi.org/10.1016/s0265-9646(98)00013-7.

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30

Walschap, Gerard. "Spacelike metric foliations." Journal of Geometry and Physics 32, no. 2 (December 1999): 97–101. http://dx.doi.org/10.1016/s0393-0440(99)00021-2.

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31

Şenyurt, Süleyman, and Sümeyye Gur. "Spacelike surface geometry." International Journal of Geometric Methods in Modern Physics 14, no. 09 (August 2, 2017): 1750118. http://dx.doi.org/10.1142/s0219887817501183.

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Анотація:

In this paper, by considering [Formula: see text] and [Formula: see text] parameter curves on spacelike surface [Formula: see text], [Formula: see text] and [Formula: see text], respectively, and any spacelike curve [Formula: see text] that passes through the intersection point of these parameter curves, we have found the Darboux instantaneous rotation vectors of Darboux trihedrons of these three curves, as follows: [Formula: see text] [Formula: see text] [Formula: see text] and we have obtained the relationship between these vectors as [Formula: see text] where [Formula: see text] and [Formula: see text] are the spacelike angles between tangent vectors of [Formula: see text] and [Formula: see text] curves, and of [Formula: see text] and [Formula: see text] curves, respectively. [Formula: see text] is the unit normal vector of the surface. Besides, we have given Euler, Liouville, Bonnet formulas and Gauss curvature of the spacelike surface with new statement.

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32

Sanmartín-López, Víctor. "Spacelike isoparametric hypersurfaces." Differential Geometry and its Applications 54 (October 2017): 53–58. http://dx.doi.org/10.1016/j.difgeo.2016.12.006.

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33

Ergüt, Mahmut, Essin Turhan, and Talat Körpınar. "Characterization of inextensible flows of spacelike curves with sabban frame in S₁²." Boletim da Sociedade Paranaense de Matemática 31, no. 2 (December 12, 2013): 47. http://dx.doi.org/10.5269/bspm.v31i2.15957.

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34

Mahmoud, W. M., and Alaa Hassan Noreldeen. "Inextensible Flows of Spacelike Curves According to Equiform Frame in 4-dimensional Minkowski Space R41." WSEAS TRANSACTIONS ON MATHEMATICS 19 (February 10, 2021): 683–98. http://dx.doi.org/10.37394/23206.2020.19.75.

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Анотація:

In this paper, we study inextensible flows of spacelike curves lying fully on a spacelike surface Ω according to equiform frame in 4-dimensional Minkowski space ℝ1 4 . We give necessary and sufficient conditions for this inextensible flows which are expressed as a partial differential equation involving the equiform curvature functions in 4-dimensional Minkowski space ℝ1 4 . Finally we give an application of inextensible flows of spacelike curves in ℝ1 4 .

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35

Nazra, Sahar H., and Rashad A. Abdel-Baky. "Time-Like Sweeping Surfaces with a Bishop Frame in the Minkowski 3-Space E 1 3." Mathematical Problems in Engineering 2022 (April 28, 2022): 1–8. http://dx.doi.org/10.1155/2022/4189643.

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Анотація:

In this paper, we consider a time-like sweeping surface and its local singularities with Bishop frame in Minkowski 3-space E 1 3 . Subsequently, we derive the sufficient and necessary conditions for this surface to be spacelike developable ruled surface. In particular, we mainly focus on the study for the resulting spacelike developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding spacelike developable surfaces.

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36

Aldossary, Maryam T., and Rashad A. Abdel-Baky. "On the Blaschke approach of Bertrand offsets of spacelike ruled surfaces." AIMS Mathematics 7, no. 10 (2022): 17843–58. http://dx.doi.org/10.3934/math.2022983.

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Анотація:

<abstract>In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike ruled and developable surfaces. It is proved that, every spacelike ruled surface have a Bertrand offset if and only if an equation should be fulfilled among their dual integral invariants. Consequently, some new relationships and theorems for the developability of the Bertrand offsets of spacelike ruled surfaces are outlined.</abstract>

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37

Kusak-Samanci, Hatice, and Huseyin Kocayigit. "N-Bishop Darboux vector of the spacelike curve with spacelike binormal." Thermal Science 23, Suppl. 1 (2019): 353–60. http://dx.doi.org/10.2298/tsci181112048k.

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Анотація:

In this article, the N-Bishop frame in Minkowski space is investigated for spacelike curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.

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38

Koc Ozturk, Esra Betul, Ufuk Ozturk, Kazim Ilarslan, and Emilija Nešović. "On Pseudospherical Smarandache Curves in Minkowski 3-Space." Journal of Applied Mathematics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/404521.

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Анотація:

In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame’s vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curveα, thenαhas constant geodesic curvature. Finally, we give some examples of pseudospherical Smarandache curves.

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39

DE LIMA, HENRIQUE FERNANDES, ANTONIO FERNANDO DE SOUSA, and MARCO ANTONIO LÁZARO VELÁSQUEZ. "STABILITY OF SPACELIKE HYPERSURFACES WITH HIGHER-ORDER MEAN CURVATURES LINEARLY RELATED IN CONFORMALLY STATIONARY SPACETIMES." International Journal of Mathematics 24, no. 14 (December 2013): 1350109. http://dx.doi.org/10.1142/s0129167x13501097.

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Анотація:

In this paper, we establish the notion of (r, s)-stability concerning spacelike hypersurfaces with higher-order mean curvatures linearly related in conformally stationary spacetimes of constant sectional curvature. In this setting, we characterize (r, s)-stable closed spacelike hypersurfaces through the analysis of the first eigenvalue of an operator naturally attached to the higher-order mean curvatures. Moreover, we obtain sufficient conditions which assure the (r, s)-stability of complete spacelike hypersurfaces immersed in the de Sitter space.

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40

LI, YANLIN, AYŞE YAVUZ, and MELEK ERDOĞDU. "SURFACES WITH VANISHING ABNORMALITY OF NORMAL DIRECTION IN MINKOWSKI SPACE." Journal of Science and Arts 22, no. 4 (December 30, 2022): 907–18. http://dx.doi.org/10.46939/j.sci.arts-22.4-a12.

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This paper is investigated geometry of vector fields along spacelike curve with timelike normal vector by using anholonomic coordinates. Derivative formulas of Frenet Serret frame of the curve are stated which includes eight parameters. Surfaces with vanishing abnormality of normal direction in Minkowski space are examined. Intrinsic geometric properties of these spacelike surfaces are investigated. Finally, the relations between spacelike surfaces with vanishing abnormality of normal direction and NLS, Heisenberg spin equation are investigated as applications.

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41

Koh, Sung-Eun. "An analytic extension of a spacelike maximal surface." Bulletin of the Australian Mathematical Society 76, no. 1 (August 2007): 43–47. http://dx.doi.org/10.1017/s0004972700039459.

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42

Bas, Selçuk, and Talat Körpınar. "Inextensible flows of spacelike curves with timelike principal normal according to Darboux frame in M₁³." Boletim da Sociedade Paranaense de Matemática 31, no. 2 (December 12, 2013): 9. http://dx.doi.org/10.5269/bspm.v31i2.15754.

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43

Baş, Selçuk. "A New Version of Spherical Magnetic Curves in the De-Sitter Space S 1 2." Symmetry 10, no. 11 (November 7, 2018): 606. http://dx.doi.org/10.3390/sym10110606.

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This paper presents a new type of spacelike magnetic curves associated with the Sabban vector field defined in the Minkowski space. In this approach, some geometrical and physical features of the moving charged particle corresponding to the spacelike magnetic curves are identified. An entire characterization is developed for spacelike spherical magnetic curves, denoting particularly the changes of their energy with respect to time, the influence of the magnetic force on them, and the existence condition for the uniformity of these curves.

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44

Nesterenko, A. V. "Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment." Journal of Physics G: Nuclear and Particle Physics 49, no. 5 (April 1, 2022): 055001. http://dx.doi.org/10.1088/1361-6471/ac5d0a.

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Abstract The complete set of relations, which mutually express the spacelike and timelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment a μ HVP in terms of each other, is obtained. By making use of the derived relations the explicit expression for the next-to-leading order spacelike kernel function, which enters the representation for a μ HVP involving the hadronic vacuum polarization function, is obtained. The corresponding next-to-leading order spacelike kernel function, which appears in the representation for a μ HVP involving the Adler function, is calculated numerically. The obtained results can be employed in the assessments of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment in the framework of the spacelike methods, such as lattice studies, MUonE project, and others.

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45

Alías, Luis J., Aldir Brasil, and A. Gervasio Colares. "INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS." Proceedings of the Edinburgh Mathematical Society 46, no. 2 (June 2003): 465–88. http://dx.doi.org/10.1017/s0013091502000500.

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AbstractIn this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike conformal field. We apply them to the study of the umbilicity of compact spacelike hypersurfaces in terms of their $r$-mean curvatures. We derive several uniqueness results, for instance, compact spacelike hypersurfaces are umbilical if either some of their $r$-mean curvatures are linearly related or one of them is constant.AMS 2000 Mathematics subject classification: Primary 53C42. Secondary 53B30; 53C50; 53Z05; 83C99

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46

Körpınar, Talat, and Essin Turhan. "Darboux rotation axis of spacelike biharmonic helices with timelike normal in the Lorentzian E(1, 1)." Boletim da Sociedade Paranaense de Matemática 31, no. 1 (October 21, 2011): 9. http://dx.doi.org/10.5269/bspm.v31i1.14872.

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In this paper, we study Darboux rotation axis for spacelike biharmonic helices in the Lorentzian group of rigid motions E(1,1). We obtain equation of Darboux vector of spacelike biharmonic helices in the Lorentzian E(1,1).

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47

Pashaie, Firooz. "Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition LkHk+1 = λHk+1". Proyecciones (Antofagasta) 40, № 3 (1 червня 2021): 711–19. http://dx.doi.org/10.22199/issn.0717-6279-3584.

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In this paper, we try to give a classification of spacelike hypersurfaces of the Lorentz-Minkowski space-time E1n+1, whose mean curvature vector field of order (k+ 1) is an eigenvector of the kth linearized operator Lk, for a non-negative integer k less than n. The operator Lk is defined as the linear part of the first variation of the (k + 1)th mean curvature of a hypersurface arising from its normal variations. We show that any spacelike hypersurface of E1n+1 satisfying the condition LkHk+1 = λHk+1 (where 0 ≤ k ≤ n − 1) belongs to the class of Lk-biharmonic, Lk-1-type or Lk-null-2-type hypersurface. Furthermore, we study the above condition on a well-known family of spacelike hypersurfaces of Lorentz-Minkowski spaces, named the weakly convex hypersurfaces (i.e. on which all of principle curvatures are nonnegative). We prove that, on any weakly convex spacelike hypersurface satisfying the above condition for an integer k (where, 0 ≤ r ≤ n−1), the (k + 1)th mean curvature will be constant. As an interesting result, any weakly convex spacelike hypersurfaces, having assumed to be Lk-biharmonic, has to be k-maximal.

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48

Liu, Haiming, Xiawei Chen, Jianyun Guan, and Peifu Zu. "Lorentzian approximations for a Lorentzian $ \alpha $-Sasakian manifold and Gauss-Bonnet theorems." AIMS Mathematics 8, no. 1 (2022): 501–28. http://dx.doi.org/10.3934/math.2023024.

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<abstract>In this paper, we define the Lorentzian approximations of a $ 3 $-dimensional Lorentzian $ \alpha $-Sasakian manifold. Moreover, we define the notions of the intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on Lorentzian surfaces and spacelike surfaces and the intrinsic Gaussian curvature of Lorentzian surfaces and spacelike surfaces away from characteristic points. Furthermore, we derive the expressions of those curvatures and prove Gauss-Bonnet theorems for the Lorentzian surfaces and spacelike surfaces in the Lorentzian $ \alpha $-Sasakian manifold.</abstract>

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49

Izumiya, Shyuichi, and Masaki Kasedou. "Lightlike flat geometry of spacelike submanifolds in Lorentz–Minkowski space." International Journal of Geometric Methods in Modern Physics 11, no. 05 (May 2014): 1450049. http://dx.doi.org/10.1142/s0219887814500492.

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In this paper, we investigate differential geometry on spacelike submanifolds in Lorentz–Minkowski space from the viewpoint of contact with lightlike hyperplanes. It is called the lightlike flat geometry which has been well established for the codimension-two case. In order to develop the theory for the general codimension-case, we introduce the notion of codimension-two spacelike canal submanifolds which is a main tool in this paper. We apply the theory of Lagrangian/Legendrian singularities to codimension-two spacelike canal submanifolds and obtain the relation with the previous results on the codimension-two case.

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50

Mofarreh, Fatemah, and Rashad A. Abdel-Baky. "Spacelike ruled surfaces with stationary Disteli-axis." AIMS Mathematics 8, no. 4 (2023): 7840–55. http://dx.doi.org/10.3934/math.2023394.

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<abstract>This paper derives the expressions for spacelike ruled surfaces with stationary Disteli-axis by means of the E. Study map. This provides the ability to compute a set of Lorentzian curvature functions which define the local shape of spacelike ruled surfaces. Consequently, some well-known formulae of surface theory at Lorentzian line space and their geometrical explanations are obtained and examined. Lastly, a characterization for a spacelike line trajectory to be a constant Disteli-axis is derived and investigated in detail.</abstract>

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