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Journal articles on the topic 'Differential geometry'

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Published: 4 June 2021
Last updated: 31 July 2024

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1

Švec, Alois. "Differential geometry of surfaces." Czechoslovak Mathematical Journal 39, no. 2 (1989): 303–22. http://dx.doi.org/10.21136/cmj.1989.102304.

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2

Kainz, Gerd, and Peter W. Michor. "Natural transformations in differential geometry." Czechoslovak Mathematical Journal 37, no. 4 (1987): 584–607. http://dx.doi.org/10.21136/cmj.1987.102187.

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3

Švec, Alois. "Affine differential geometry of surfaces." Czechoslovak Mathematical Journal 40, no. 1 (1990): 125–54. http://dx.doi.org/10.21136/cmj.1990.102365.

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4

Willmore, T. J. "DIFFERENTIAL GEOMETRY." Bulletin of the London Mathematical Society 21, no. 1 (January 1989): 103–4. http://dx.doi.org/10.1112/blms/21.1.103.

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5

Landsberg, J. M. "differential geometry." Duke Mathematical Journal 85, no. 3 (December 1996): 605–34. http://dx.doi.org/10.1215/s0012-7094-96-08523-3.

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6

Trautman, Andrzej, William L. Burke, and Emil Kazes. "Differential Geometry for Physicists and Applied Differential Geometry." Physics Today 39, no. 5 (May 1986): 88–90. http://dx.doi.org/10.1063/1.2815009.

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7

Kock, Anders. "Differential Calculus and Nilpotent Real Numbers." Bulletin of Symbolic Logic 9, no. 2 (June 2003): 225–30. http://dx.doi.org/10.2178/bsl/1052669291.

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Do there exist real numbers d with d2 = 0 (besides d = 0, of course)? The question is formulated provocatively, to stress a formalist view about existence: existence is consistency, or better, coherence.Also, the provocation is meant to challenge the monopoly which the number system, invented by Dedekind et al., is claiming for itself as THE model of the geometric line. The Dedekind approach may be termed “arithmetization of geometry”.We know that one may construct a number system out of synthetic geometry, as Euclid and followers did (completed in Hilbert's Grundlagen der Geometrie, [2, Chapter 3]): “geometrization of arithmetic”. (Picking two distinct points on the geometric line, geometric constructions in an ambient Euclidean plane provide structure of a commutative ring on the line, with the two chosen points as 0 and 1).Starting from the geometric side, nilpotent elements are somewhat reasonable, although Euclid excluded them. The sophist Protagoras presented a picture of a circle and a tangent line; the apparent little line segment D which tangent and circle have in common, are, by Pythagoras' Theorem, precisely the points, whose abscissae d (measured along the tangent) have d2 = 0. Protagoras wanted to use this argument for destructive reasons: to refute the science of geometry.A couple of millenia later, the Danish geometer Hjelmslev revived the Protagoras picture. His aim was more positive: he wanted to describe Nature as it was. According to him (or extrapolating his position), the Real Line, the Line of Sensual Reality, had many nilpotent infinitesimals, which we can see with our naked eyes.
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8

Frittelli, Simonetta, Carlos Kozameh, and Ezra T. Newman. "Differential Geometry from Differential Equations." Communications in Mathematical Physics 223, no. 2 (October 1, 2001): 383–408. http://dx.doi.org/10.1007/s002200100548.

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9

Yang, Deane, and William L. Burke. "Applied Differential Geometry." American Mathematical Monthly 95, no. 10 (December 1988): 964. http://dx.doi.org/10.2307/2322407.

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10

Banchoff, Thomas F., and S. S. Chern. "Global Differential Geometry." American Mathematical Monthly 98, no. 7 (August 1991): 669. http://dx.doi.org/10.2307/2324949.

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11

Giblin, Peter, and Andrew Pressley. "Elementary Differential Geometry." Mathematical Gazette 85, no. 503 (July 2001): 372. http://dx.doi.org/10.2307/3622071.

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12

Bobenko, Alexander, Richard Kenyon, Peter Schröder, and Günter Ziegler. "Discrete Differential Geometry." Oberwolfach Reports 9, no. 3 (2012): 2077–137. http://dx.doi.org/10.4171/owr/2012/34.

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13

Bobenko, Alexander, Richard Kenyon, and Peter Schröder. "Discrete Differential Geometry." Oberwolfach Reports 12, no. 1 (2015): 661–729. http://dx.doi.org/10.4171/owr/2015/13.

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14

Crasmareanu, Mircea, and Cristina-Elena Hreţcanu. "Golden differential geometry☆." Chaos, Solitons & Fractals 38, no. 5 (December 2008): 1229–38. http://dx.doi.org/10.1016/j.chaos.2008.04.007.

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15

Desbrun, Mathieu, and Konrad Polthier. "Discrete Differential Geometry." Computer Aided Geometric Design 24, no. 8-9 (November 2007): 427. http://dx.doi.org/10.1016/j.cagd.2007.07.005.

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16

Ravishanker, Nalini. "DIFFERENTIAL GEOMETRY OFARFIMAPROCESSES." Communications in Statistics - Theory and Methods 30, no. 8-9 (July 31, 2001): 1889–902. http://dx.doi.org/10.1081/sta-100105703.

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17

KoláŘ, Ivan. "Applicable differential geometry." Acta Applicandae Mathematicae 18, no. 1 (January 1990): 88–89. http://dx.doi.org/10.1007/bf00822209.

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18

Rédl, J., and V. Váliková. "Application of differential geometry in agricultural vehicle dynamics." Research in Agricultural Engineering 59, Special Issue (December 13, 2013): S34—S41. http://dx.doi.org/10.17221/49/2012-rae.

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This paper deals with the application of differential geometry methods to a precise calculation of the length of trajectory of an agricultural mechanism that moves on a sloping terrain. We obtained technical exciting function from experimental measurements, out of which we obtained the function of Euler’s parameters by using computer processing. The processing of these parameters provided translational and angular velocities of the gravity centre of the systemic vehicle MT8-222, which performed the determined mounted manoeuvres. We obtained differential equations that describe the function of a spatial curve by the application of differential geometry methods. The length of the curve is obtained by a numerical solution of the differential equations formed. We used Dormand-Prince numerical method for the numerical solution. Next, we evaluated the error of the numerical integration for every calculation by reason of the stability of computation. We also addressed the geometric characteristics of the curves such as the radius of curvature. The mounted manoeuvres as well as the corresponding velocities, trajectories, and radiuses of curvature were processed in a graphic way.
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19

Abdel Rahman, Abdel Radi Abdel Rahman Abdel Gadir, Adam Haroun Ishag Gary, and Anoud Hassan Elzain Ageeb. "SOME APPLICATIONS OF SECTIONAL CURVATURE IN DIFFERENTIAL GEOMETRY." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 02 (February 16, 2023): 3236–42. http://dx.doi.org/10.47191/ijmcr/v11i2.02.

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The applications of the differential geometry of sectional curvature plays a great role in the field of physics, mathematics and engineering because it paves to knowledge of curves, surfaces, curvature, radius of curvature and sectional curvature . The study aims to explain some applications of sectional curvature. We followed the analytical induction mathematical method. We found the following some result: The sectional curvature indicate to know the behavior of some the functions and also we found that the sectional curvature is the Gaussian curvature.
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20

NISHIMURA, HIROKAZU. "Axiomatic differential geometry I-1 - towards model categories of differential geometry." MATHEMATICS FOR APPLICATIONS 1, no. 2 (December 20, 2012): 171–82. http://dx.doi.org/10.13164/ma.2012.11.

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21

Lipták, Tomáš, Alexander Gmiterko, Michal Kelemen, Ivan Virgala, Erik Prada, and František Menda. "Theoretical Basics of Geometric Mechanics and Differential Geometry." American Journal of Mechanical Engineering 2, no. 7 (November 15, 2014): 178–83. http://dx.doi.org/10.12691/ajme-2-7-1.

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22

Bulut, Vahide. "Differential geometry of autonomous wheel-legged robots." Engineering Computations 37, no. 2 (September 6, 2019): 615–37. http://dx.doi.org/10.1108/ec-11-2018-0546.

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Purpose The purpose of this study is to obtain the differential geometric analysis of autonomous wheel-legged robots and their trajectories on the terrain. Design/methodology/approach The author uses a wheel using the osculating sphere of the curve on rough terrain. Additionally, the author expresses a triple osculating sphere wheel by taking advantage of differential geometry. Moreover, the author examined the consecutive wheel center-curves to obtain the optimum posture of a micro-hydraulic toolkit (MHT) robot. Findings The author examined the terrain path, which is crucial for trajectory planning in terms of the geometric perspective. The author designed the triple MHT wheel using the osculating sphere of the MHT robot trajectory by taking advantage of local differential geometric properties of this curve on the terrain. The consecutive wheel center-curves were expressed and studied based on differential geometry. Originality/value The author provides a novel approach for the optimum posture of an MHT robot using consecutive wheel-center curves and provides an original perspective to MHT robot and its trajectory by using differential geometry.
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23

Marriott, P. K., M. K. Murray, and J. W. Rice. "Differential Geometry and Statistics." Mathematical Gazette 78, no. 482 (July 1994): 237. http://dx.doi.org/10.2307/3618610.

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24

Murray, M. K., and J. W. Rice. "Differential Geometry and Statistics." Biometrics 51, no. 4 (December 1995): 1588. http://dx.doi.org/10.2307/2533302.

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25

Marriott, Paul. "DIFFERENTIAL GEOMETRY AND STATISTICS." Bulletin of the London Mathematical Society 27, no. 6 (November 1995): 619–20. http://dx.doi.org/10.1112/blms/27.6.619.

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26

Connes, Alain. "Non-commutative differential geometry." Publications mathématiques de l'IHÉS 62, no. 1 (December 1985): 41–144. http://dx.doi.org/10.1007/bf02698807.

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27

Rota, Gian-Carlo. "Differential geometry of foliations." Advances in Mathematics 57, no. 1 (July 1985): 91. http://dx.doi.org/10.1016/0001-8708(85)90109-4.

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28

Stolyarov, A. V. "Differential Geometry of Distributions." Journal of Mathematical Sciences 207, no. 4 (May 1, 2015): 635–57. http://dx.doi.org/10.1007/s10958-015-2387-4.

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29

Donaldson, Simon. "Yau and differential geometry." Notices of the International Congress of Chinese Mathematicians 7, no. 1 (2019): 28–29. http://dx.doi.org/10.4310/iccm.2019.v7.n1.a12.

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30

Seshadri, Harish. "Differential geometry in India." Indian Journal of Pure and Applied Mathematics 50, no. 3 (August 20, 2019): 795–99. http://dx.doi.org/10.1007/s13226-019-0355-2.

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31

Kulish, P. P. "Covariant noncommutative differential geometry." Journal of Mathematical Sciences 80, no. 3 (June 1996): 1811–17. http://dx.doi.org/10.1007/bf02362779.

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32

Liu, Xin-Guo, Hu-Jun Bao, and Qun-Sheng Peng. "Digital Differential Geometry Processing." Journal of Computer Science and Technology 21, no. 5 (September 2006): 847–60. http://dx.doi.org/10.1007/s11390-006-0847-5.

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33

Breen, Lawrence, and William Messing. "Differential geometry of gerbes." Advances in Mathematics 198, no. 2 (December 2005): 732–846. http://dx.doi.org/10.1016/j.aim.2005.06.014.

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34

Loizides, Yiannis, and Eckhard Meinrenken. "Differential geometry of weightings." Advances in Mathematics 424 (July 2023): 109072. http://dx.doi.org/10.1016/j.aim.2023.109072.

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35

Donaldson, S. K. "SURVEYS IN DIFFERENTIAL GEOMETRY (Supplement to the Journal of Differential Geometry 1)." Bulletin of the London Mathematical Society 27, no. 5 (September 1995): 497–99. http://dx.doi.org/10.1112/blms/27.5.497.

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36

FRITTELLI, S., N. KAMRAN, C. KOZAMEH, and E. T. NEWMAN. "NULL SURFACES AND CONTACT GEOMETRY." Journal of Hyperbolic Differential Equations 02, no. 02 (June 2005): 481–96. http://dx.doi.org/10.1142/s0219891605000506.

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We give a self-contained and geometric account of a recent approach to the Einstein field equations of general relativity, based on families of null foliations of space–time. We then use exterior differential systems to make explicit the correspondence between conformal Lorentzian geometry in dimensions three and four and the contact geometry of special classes of differential systems.
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37

Vondra, Alexandr. "Geometry of second-order connections and ordinary differential equations." Mathematica Bohemica 120, no. 2 (1995): 145–67. http://dx.doi.org/10.21136/mb.1995.126226.

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38

NISHIMURA, HIROKAZU. "Axiomatic differential geometry II-2 - differential forms." MATHEMATICS FOR APPLICATIONS 2, no. 1 (June 20, 2013): 43–60. http://dx.doi.org/10.13164/ma.2013.05.

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39

Nielsen, Frank. "An Elementary Introduction to Information Geometry." Entropy 22, no. 10 (September 29, 2020): 1100. http://dx.doi.org/10.3390/e22101100.

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In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity.
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40

Navickis, Kazimieras. "Affine differential geometry of osculating hypersurfaces." Lietuvos matematikos rinkinys 53 (December 25, 2012): 37–41. http://dx.doi.org/10.15388/lmr.b.2012.07.

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Osculating surfaces of second order have been studied in classical affine differential geometry [1]. In this article we generalize this notion to osculating hypersurfaces of higher order of hypersurfaces in Euclidean n-space. Various geometric interpretations are given. This yields a affinely invariant consideration of the local properties of a given hypersurface which depend on the derivatives of higher order.
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41

Chen, Bang-Yen. "Differential Geometry of Identity Maps: A Survey." Mathematics 8, no. 8 (August 2, 2020): 1264. http://dx.doi.org/10.3390/math8081264.

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An identity map idM:M→M is a bijective map from a manifold M onto itself which carries each point of M return to the same point. To study the differential geometry of an identity map idM:M→M, we usually assume that the domain M and the range M admit metrics g and g′, respectively. The main purpose of this paper is to provide a comprehensive survey on the differential geometry of identity maps from various differential geometric points of view.
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42

Goto, Shin-itiro. "Affine geometric description of thermodynamics." Journal of Mathematical Physics 64, no. 1 (January 1, 2023): 013301. http://dx.doi.org/10.1063/5.0124768.

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Thermodynamics provides a unified perspective of the thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described by a variety of differential geometries, including contact and symplectic geometries. Meanwhile, affine geometry is a branch of differential geometry and is compatible with information geometry, where information geometry is known to be compatible with thermodynamics. By combining above, it is expected that thermodynamics is compatible with affine geometry and is expected that several affine geometric tools can be introduced in the analysis of thermodynamic systems. In this paper, affine geometric descriptions of equilibrium and nonequilibrium thermodynamics are proposed. For equilibrium systems, it is shown that several thermodynamic quantities can be identified with geometric objects in affine geometry and that several geometric objects can be introduced in thermodynamics. Examples of these include the following: specific heat is identified with the affine fundamental form and a flat connection is introduced in thermodynamic phase space. For nonequilibrium systems, two classes of relaxation processes are shown to be described in the language of an extension of affine geometry. Finally, this affine geometric description of thermodynamics for equilibrium and nonequilibrium systems is compared with a contact geometric description.
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43

Wang, Changping. "Surfaces in Möbius geometry." Nagoya Mathematical Journal 125 (March 1992): 53–72. http://dx.doi.org/10.1017/s0027763000003895.

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Our purpose in this paper is to give a basic theory of Möbius differential geometay. In such geometry we study the properties of hypersurfaces in unit sphere Sn which are invariant under the Möbius transformation group on Sn.Since any Möbius transformation takes oriented spheres in Sn to oriented spheres, we can regard the Möbius transformation group Gn as a subgroup MGn of the Lie transformation group on the unit tangent bundle USn of Sn. Furthermore, we can represent the immersed hypersurfaces in Sn by a class of Lie geometry hypersurfaces (cf. [9]) called Möbius hypersurfaces. Thus we can use the concepts and the techniques in Lie sphere geometry developed by U. Pinkall ([8], [9]), T. Cecil and S. S. Chern [2] to study the Möbius differential geometry.
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44

Maißer, P. "Multi-body dynamics and electromechanics: From a differential-geometric point of view." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 219, no. 2 (June 1, 2005): 147–58. http://dx.doi.org/10.1243/146441905x34135.

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Mechanics is the origin of physics. Almost any physical theory like electrodynamics stems from mechanical explanations. The mathematical-geometric considerations in mechanics serve as a prototype for other physical theories. Consequently, developments in modern physics in turn have a feedback to mechanics in terms of its representation. The laws of nature can be expressed as differential equations. The fact that these equations can be solved by average computers has led most engineers and many mathematical physicists to neglect geometrical aspects for solving and better understanding their problems. The intimate relation between geometry and analysis led to the differential geometry, which is a valuable tool for a better understanding in many physical disciplines like classical mechanics, electrodynamics, and nowadays in mechatronics. It has been the development of the theory of relativity that revealed the paramount importance of the differential geometry. Many problems in research and development can be studied by differential-geometric methods. Modern non-linear control theories, for instance, are entirely based on the differential geometry. This paper addresses some aspects in mathematical modelling of multi-body and electromechanical systems. The motivation for this research arises from applications of linear induction machines in modern transport technologies.
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45

OTSUKI, Tominosuke. "ON A DIFFERENTIAL EQUATION RELATED WITH DIFFERENTIAL GEOMETRY." Memoirs of the Faculty of Science, Kyusyu University. Series A, Mathematics 47, no. 2 (1993): 245–81. http://dx.doi.org/10.2206/kyushumfs.47.245.

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46

Calviño-Louzao, Esteban, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, and Ramón Vázquez-Lorenzo. "Aspects of Differential Geometry V." Synthesis Lectures on Mathematics and Statistics 13, no. 3 (April 5, 2021): 1–156. http://dx.doi.org/10.2200/s01085ed1v05y202104mas041.

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47

Osserman, Robert, and Heinz Hopf. "Differential Geometry in the Large." American Mathematical Monthly 93, no. 1 (January 1986): 71. http://dx.doi.org/10.2307/2322562.

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48

Thorpe, John A., Richard L. Faber, and Barrett O'Neill. "Differential Geometry and Relativity Theory." American Mathematical Monthly 93, no. 7 (August 1986): 575. http://dx.doi.org/10.2307/2323053.

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49

CHEN, Bang-yen. "Differential Geometry of Rectifying Submanifolds." International Electronic Journal of Geometry 9, no. 2 (October 30, 2016): 1–8. http://dx.doi.org/10.36890/iejg.584566.

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50

Rosensteel, George. "Differential geometry of collective models." AIMS Mathematics 4, no. 2 (2019): 215–30. http://dx.doi.org/10.3934/math.2019.2.215.

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