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Relevant bibliographies by topics / Congruences (Geometry) Geometry, Differential / Journal articles

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Journal articles on the topic 'Congruences (Geometry) Geometry, Differential'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Иванов, Геннадий, and Gennadiy Ivanov. "Construction of Belonging to Surfaces One-Dimensional Contours by Mapping Them to a Plane." Geometry & Graphics 6, no. 1 (2018): 3–9. http://dx.doi.org/10.12737/article_5ad07ed61bc114.52669586.

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As is known, differential geometry studies the properties of curve lines (tangent, curvature, torsion), surfaces (bending, first and second basic quadratic forms) and their families in small, that is, in the neighborhood of the point by means of differential calculus. Algebraic geometry studies properties of algebraic curves, surfaces, and algebraic varieties in general [1; 17]: order, class, genre, existence of singular points and lines, curves and surfaces family intersections (sheaves, bundles, congruences, complexes and their characteristics). Rational curves and surfaces occupy a special

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2

Alluhaibi, Nadia, and R. A. Abdel-Baky. "On the one-parameter Lorentzian spatial motions." International Journal of Geometric Methods in Modern Physics 16, no. 12 (2019): 1950197. http://dx.doi.org/10.1142/s0219887819501974.

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In this paper, differential properties of the one-parameter Lorentzian spatial motions are developed with explicit expressions independent of coordinates systems. In term of this, we calculate the Disteli formulae of a spacelike line trajectory and derive the connections with kinematic geometry of the axodes. Lastly, a theoretical expression of a spacelike inflection line congruence are investigated in detail.

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3

Умбетов, Nurlan Umbetov, Джанабаев, and Zh Dzhanabaev. "On Algorithms of Graphical Plotting of Geodesic Line on a Ruled Surface." Geometry & Graphics 3, no. 4 (2015): 15–18. http://dx.doi.org/10.12737/17346.

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Geodesic lines find interesting applications when solving many tasks of fundamental sciences (mathematicians, physics, etc.) and engineering practice. In differential geometry geodesic lines are characteristic lines for determination of internal properties of surface. However, the construction of geodesic line on a surface presents certain complications, mainly solved by the methods of calculating mathematics and descriptive geometry. In this article the development of a simple and comfortable algorithm of construction of geodesic line is considered on linear surfaces. In general case, the spa

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4

Willmore, T. J. "DIFFERENTIAL GEOMETRY." Bulletin of the London Mathematical Society 21, no. 1 (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 (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 (1986): 88–90. http://dx.doi.org/10.1063/1.2815009.

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7

Grünberg, Daniel B., Pieter Moree, and Don Zagier. "Sequences of Enumerative Geometry: Congruences and Asymptotics." Experimental Mathematics 17, no. 4 (2008): 409–26. http://dx.doi.org/10.1080/10586458.2008.10128870.

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8

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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9

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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10

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

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11

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

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12

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

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13

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

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14

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

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15

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

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16

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

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17

Hill, C. Denson, and Paweł Nurowski. "Intrinsic geometry of oriented congruences in three dimensions." Journal of Geometry and Physics 59, no. 2 (2009): 133–72. http://dx.doi.org/10.1016/j.geomphys.2008.10.001.

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18

Ponce, Jean, Bernd Sturmfels, and Mathew Trager. "Congruences and concurrent lines in multi-view geometry." Advances in Applied Mathematics 88 (July 2017): 62–91. http://dx.doi.org/10.1016/j.aam.2017.01.001.

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19

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

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20

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

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21

Dempsey, David, and Sam R. Dolan. "Waves and null congruences in a draining bathtub." International Journal of Modern Physics D 25, no. 09 (2016): 1641004. http://dx.doi.org/10.1142/s0218271816410042.

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We study wave propagation in a draining bathtub: a black hole analogue in fluid mechanics whose perturbations are governed by a Klein–Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possesses an (effective) horizon, an ergosphere and null circular orbits. We propose here that a ‘pulse’ disturbance may be used to map out the light-cone of the effective geometry. First, we apply the eikonal approximation to elucidate the link between wavefronts, null geodesic congruences and the Raychaudhuri equation. Next, we solve the wave equation nu

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22

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

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23

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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24

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

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25

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

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26

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

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27

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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28

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

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29

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

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30

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

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31

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

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32

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

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33

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

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34

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

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35

Ciaglia, F. M., G. Marmo, and J. M. Pérez-Pardo. "Generalized potential functions in differential geometry and information geometry." International Journal of Geometric Methods in Modern Physics 16, supp01 (2019): 1940002. http://dx.doi.org/10.1142/s0219887819400024.

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Potential functions can be used for generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study whether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.

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36

Zimpel, Zbigniew, and Paul G. Mezey. "Molecular geometry and symmetry from a differential geometry viewpoint." International Journal of Quantum Chemistry 64, no. 6 (1997): 669–78. http://dx.doi.org/10.1002/(sici)1097-461x(1997)64:6<669::aid-qua4>3.0.co;2-u.

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37

Hosono, Shinobu, and Hiromichi Takagi. "Mirror symmetry and projective geometry of Reye congruences I." Journal of Algebraic Geometry 23, no. 2 (2013): 279–312. http://dx.doi.org/10.1090/s1056-3911-2013-00618-9.

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38

Doliwa, Adam. "Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry." Journal of Nonlinear Mathematical Physics 8, sup1 (2001): 88–92. http://dx.doi.org/10.2991/jnmp.2001.8.s.16.

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39

DOLIWA, Adam. "Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry." Journal of Non-linear Mathematical Physics 8, Supplement (2001): 88. http://dx.doi.org/10.2991/jnmp.2001.8.supplement.16.

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40

Alekseevsky, Dmitri V., Masoud Ganji, Gerd Schmalz, and Andrea Spiro. "Lorentzian manifolds with shearfree congruences and Kähler-Sasaki geometry." Differential Geometry and its Applications 75 (April 2021): 101724. http://dx.doi.org/10.1016/j.difgeo.2021.101724.

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41

Bobenko, Alexander I., and Yury B. Suris. "On organizing principles of discrete differential geometry. Geometry of spheres." Russian Mathematical Surveys 62, no. 1 (2007): 1–43. http://dx.doi.org/10.1070/rm2007v062n01abeh004380.

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42

GIRALDO, LUIS, and IGNACIO SOLS. "Chow forms of congruences." Mathematical Proceedings of the Cambridge Philosophical Society 121, no. 1 (1997): 31–37. http://dx.doi.org/10.1017/s0305004196001302.

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Let V be a 4-dimensional complex space. A congruence Y is an integral surface of the Grassmann variety G = Gr(2, 4) of 2-dimensional subspaces V2 of V (we denote by Vi a subspace of V of dimension i). They have been extensively studied by both classical and modern geometers. We bring to their study the tool of Chow forms, characterizing them by differential equations, following the program of M. Green and I. Morrison [3]. The first results in this direction are due to Cayley ([1], [2]) and are rederived in [3]. Our results share much of the geometrical flavour of Cayley's.

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43

Jankovský, Zdeněk. "Laguerre's differential geometry and kinematics." Mathematica Bohemica 120, no. 1 (1995): 29–40. http://dx.doi.org/10.21136/mb.1995.125894.

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44

Kim, Young-Wook, and Hyoung-Yong Lee. "CONVERGENCE IN METRIC DIFFERENTIAL GEOMETRY." Communications of the Korean Mathematical Society 18, no. 1 (2003): 87–94. http://dx.doi.org/10.4134/ckms.2003.18.1.087.

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45

Dubrovin, Boris. "Differential geometry of moduli spaces." Surveys in Differential Geometry 4, no. 1 (1998): 213–38. http://dx.doi.org/10.4310/sdg.1998.v4.n1.a5.

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46

Donaldson, S. K. "Moment maps in differential geometry." Surveys in Differential Geometry 8, no. 1 (2003): 171–89. http://dx.doi.org/10.4310/sdg.2003.v8.n1.a6.

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47

Huhtanen, Marko. "Differential geometry of matrix inversion." MATHEMATICA SCANDINAVICA 107, no. 2 (2010): 267. http://dx.doi.org/10.7146/math.scand.a-15155.

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Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as being equivalent to a Jordan subalgebra. Global measures of curvature are introduced in terms of an analogy of the Nash fiber.

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48

Salamon, S. M. "Differential geometry of quaternionic manifolds." Annales scientifiques de l'École normale supérieure 19, no. 1 (1986): 31–55. http://dx.doi.org/10.24033/asens.1503.

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49

Barabanov, Nikita E., and Abraham A. Ungar. "Differential Geometry and Binary Operations." Symmetry 12, no. 9 (2020): 1525. http://dx.doi.org/10.3390/sym12091525.

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We derive a large set of binary operations that are algebraically isomorphic to the binary operation of the Beltrami–Klein ball model of hyperbolic geometry, known as the Einstein addition. We prove that each of these operations gives rise to a gyrocommutative gyrogroup isomorphic to Einstein gyrogroup, and satisfies a number of nice properties of the Einstein addition. We also prove that a set of cogyrolines for the Einstein addition is the same as a set of gyrolines of another binary operation. This operation is found directly and it turns out to be commutative. The same results are obtained

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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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