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Journal articles on the topic 'Riemannian geometry'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Rylov, Yuri A. "Geometry without topology as a new conception of geometry." International Journal of Mathematics and Mathematical Sciences 30, no. 12 (2002): 733–60. http://dx.doi.org/10.1155/s0161171202012243.

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A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian conception of geometry, and they are derivative in the T-geometric one. T-geometry is the simplest geometric conception (essentially, only finite point sets are investigated) and simultaneously, it is the most general one. It is insensitive to the s

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2

Wu, H., and Wilhelm Klingenberg. "Riemannian Geometry." American Mathematical Monthly 92, no. 7 (1985): 519. http://dx.doi.org/10.2307/2322529.

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3

Lord, Nick, M. P. do Carmo, S. Gallot, et al. "Riemannian Geometry." Mathematical Gazette 79, no. 486 (1995): 623. http://dx.doi.org/10.2307/3618122.

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4

Mrugała, R. "Riemannian geometry." Reports on Mathematical Physics 27, no. 2 (1989): 283–85. http://dx.doi.org/10.1016/0034-4877(89)90011-6.

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5

Shen, Zhongmin. "On Some Non-Riemannian Quantities in Finsler Geometry." Canadian Mathematical Bulletin 56, no. 1 (2013): 184–93. http://dx.doi.org/10.4153/cmb-2011-163-4.

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AbstractIn 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 study a new non-Riemannian quantity defined by the S-curvature. We show some relationships among the flag curvature, the S-curvature, and the new non-Riemannian quantity.

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6

Bhatia, Rajendra, and John Holbrook. "Riemannian geometry and matrix geometric means." Linear Algebra and its Applications 413, no. 2-3 (2006): 594–618. http://dx.doi.org/10.1016/j.laa.2005.08.025.

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7

Ehm, Werner, and Jiří Wackermann. "Geometric–optical illusions and Riemannian geometry." Journal of Mathematical Psychology 71 (April 2016): 28–38. http://dx.doi.org/10.1016/j.jmp.2016.01.005.

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8

García-Río, Eduardo, and M. Elena Vázquez-Abal. "Geodesic reflections in semi-Riemannian geometry." Czechoslovak Mathematical Journal 43, no. 4 (1993): 583–97. http://dx.doi.org/10.21136/cmj.1993.128439.

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9

M.Osman, Mohamed. "Differentiable Riemannian Geometry." International Journal of Mathematics Trends and Technology 29, no. 1 (2016): 45–55. http://dx.doi.org/10.14445/22315373/ijmtt-v29p508.

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10

Dimakis, Aristophanes, and Folkert Müller-Hoissen. "Discrete Riemannian geometry." Journal of Mathematical Physics 40, no. 3 (1999): 1518–48. http://dx.doi.org/10.1063/1.532819.

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11

Beggs, Edwin J., and Shahn Majid. "Poisson–Riemannian geometry." Journal of Geometry and Physics 114 (April 2017): 450–91. http://dx.doi.org/10.1016/j.geomphys.2016.12.012.

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12

Strichartz, Robert S. "Sub-Riemannian geometry." Journal of Differential Geometry 24, no. 2 (1986): 221–63. http://dx.doi.org/10.4310/jdg/1214440436.

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13

Mattes, M., and M. Sorg. "Riemann - Cartan Geometry of Trivializable Gauge Fields." Zeitschrift für Naturforschung A 44, no. 3 (1989): 222–38. http://dx.doi.org/10.1515/zna-1989-0309.

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A Riemann-Cartan structure can be associated to any SO (4) trivializable gauge field. Under certain integrability conditions, this non-Riemannian geometry may be replaced by a strictly Riemannian one. The Yang-Mills equations guarantee the existence of such a Riemannian structure. The general SO(4) trivializable solution for the SO(3) Yang-Mills equations is discussed within the geometric approach.

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14

Jesus, W. D. R., and A. F. Santos. "On causality violation in Lyra Geometry." International Journal of Geometric Methods in Modern Physics 15, no. 08 (2018): 1850143. http://dx.doi.org/10.1142/s0219887818501438.

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In this paper, the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein field equations are considered. It is verified that the Gödel and Gödel-type metric are consistent with this non-Riemannian geometry. A non-trivial solution for Gödel universe in the absence of matter sources is determined without analogue in general relativity. Different sources are considered and then different conditions for causal and non-causal soluti

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15

Álvarez, López Jesús Antonio, and Lijó Ramón Barral. "Bounded geometry and leaves." Mathematische Nachrichten 290 (January 9, 2017): 1448–69. https://doi.org/10.5281/zenodo.10644187.

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16

Kumar, Sushil, Rajendra Prasad та Punit Kumar Singh. "CSI-ξ^⊥-Riemannian maps from Kenmotsu manifolds to Riemannian manifolds". Gulf Journal of Mathematics 15, № 2 (2023): 96–108. http://dx.doi.org/10.56947/gjom.v15i2.1601.

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In this article, we take into account a new class of semi-invariant ξ⊥-Riemannian maps, namely, CSI-ξ⊥ (Clairaut semi-invariant-ξ⊥)-Riemannian maps in contact geometry and discuss CSI-ξ⊥-Riemannian maps from Kenmotsu manifolds to Riemannian manifolds. We extend the notion of semi-invariant ξ⊥-Riemannian maps to CSI-ξ⊥-Riemannian maps and obtain a necessary and sufficient condition for this extension. We also investigate some geometric properties of these maps and exhibit a non-trivial example of discussed maps.

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17

Ballmann, Werner. "Book Review: Riemannian Geometry and Geometric Analysis." Bulletin of the American Mathematical Society 37, no. 04 (2000): 459–66. http://dx.doi.org/10.1090/s0273-0979-00-00869-7.

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18

BEJANCU, AUREL. "A LINEAR CONNECTION FOR BOTH SUB-RIEMANNIAN GEOMETRY AND NONHOLONOMIC MECHANICS (I)." International Journal of Geometric Methods in Modern Physics 08, no. 04 (2011): 725–52. http://dx.doi.org/10.1142/s0219887811005361.

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We study the geometry of a sub-Riemannian manifold (M, HM, VM, g), where HM and VM are the horizontal and vertical distribution respectively, and g is a Riemannian extension of the Riemannian metric on HM. First, without the assumption that HM and VM are orthogonal, we construct a sub- Riemannian connection ▽ on HM and prove some Bianchi identities for ▽. Then, we introduce the horizontal sectional curvature, prove a Schur theorem for sub-Riemannian geometry and find a class of sub-Riemannian manifolds of constant horizontal curvature. Finally, we define the horizontal Ricci tensor and scalar

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19

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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20

Chinor, Makur Makuac, Mohamed Y. A. Bakhet, and Abdelmajid Ali Dafallah. "On Some Role of Riemannian Geometry." Asian Research Journal of Mathematics 19, no. 5 (2023): 51–60. http://dx.doi.org/10.9734/arjom/2023/v19i5659.

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This paper examines the mathematical significance of Riemannian geometry, including surfaces, Riemannian curvature, Gauss curvature, manifolds, geodesics, and the relationships between them. It also explores the applications of Riemannian geometry in various concepts.

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21

Sari, Ramazan, та Mehmet Akyol. "Hemi-slant ξ⊥-Riemannian submersions in contact geometry". Filomat 34, № 11 (2020): 3747–58. http://dx.doi.org/10.2298/fil2011747s.

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M. A. Akyol and R. Sar? [On semi-slant ??-Riemannian submersions, Mediterr. J. Math. 14(6) (2017) 234.] defined semi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant ??-Riemannian submersions, semi-invariant ??-Riemannian submersions and slant submersions, we study hemi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to b

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22

Greene, Robert E. "Book Review: Riemannian geometry." Bulletin of the American Mathematical Society 21, no. 1 (1989): 157–63. http://dx.doi.org/10.1090/s0273-0979-1989-15802-3.

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23

Kunzinger, Michael, and Roland Steinbauer. "Generalized pseudo-Riemannian geometry." Transactions of the American Mathematical Society 354, no. 10 (2002): 4179–99. http://dx.doi.org/10.1090/s0002-9947-02-03058-1.

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24

Larsen, Jens Chr. "Singular semi-riemannian geometry." Journal of Geometry and Physics 9, no. 1 (1992): 3–23. http://dx.doi.org/10.1016/0393-0440(92)90023-t.

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25

TAVAKOL, REZA. "GEOMETRY OF SPACETIME AND FINSLER GEOMETRY." International Journal of Modern Physics A 24, no. 08n09 (2009): 1678–85. http://dx.doi.org/10.1142/s0217751x09045224.

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A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still remain compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural metrical generalization of the Riemannian geometry, that are strictly compatible with

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26

Dr., Gyanvendra Pratap Singh, and Gaur Sapana. "A Brief Review of Differential Geometry of Manifolds." International Journal of Scientific Development and Research 9, no. 5 (2024): 469–75. https://doi.org/10.5281/zenodo.11213687.

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Riemannian geometry is the study of manifolds endowed with Riemannian matrices which are roughly speaking, rules for measuring lengths of lengths of tangent vectors and angles between them. It is the most &quot;geometric&quot; branch of differentiable geometry: This paper gives an overview about the tools we use to understand how to adapt concepts such as the distance between two points, the angle between two crossing curves curvature of a plane curve, to a surface.

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27

Youssef, Nabil L., and Ebtsam H. Taha. "Connections in sub-Riemannian geometry of parallelizable distributions." International Journal of Geometric Methods in Modern Physics 14, no. 03 (2017): 1750039. http://dx.doi.org/10.1142/s0219887817500396.

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The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint of absolute parallelism geometry and sub-Riemannian geometry. Two remarkable linear connections have been constructed on a sub-Riemannian parallelizable distribution, namely, the Weitzenböck connection and the sub-Riemannian connection. The obtained results have been applied to two concrete examples: the spheres [Formula: see text] and [Formula: see text].

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28

Sayar, Cem, Mehmet Akif Akyol, and Rajendra Prasad. "Bi-slant submersions in complex geometry." International Journal of Geometric Methods in Modern Physics 17, no. 04 (2020): 2050055. http://dx.doi.org/10.1142/s0219887820500553.

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In this paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We mainly focus on bi-slant submersions from Kaehler manifolds. We provide a proper example of bi-slant submersion, investigate the geometry of foliations determined by vertical and horizontal distributions, and obtain the geometry of leaves of these distributions. Moreover, we obtain curvature relations between the base space, the total space and the fibers, and find

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29

Calviño-Louzao, E., E. García-Río, P. Gilkey, and R. Vázquez-Lorenzo. "The geometry of modified Riemannian extensions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2107 (2009): 2023–40. http://dx.doi.org/10.1098/rspa.2009.0046.

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We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry.

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30

Al-Dayel, Ibrahim, Foued Aloui, and Sharief Deshmukh. "Geometry of Tangent Poisson–Lie Groups." Mathematics 11, no. 1 (2023): 240. http://dx.doi.org/10.3390/math11010240.

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Let G be a Poisson–Lie group equipped with a left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on G to the tangent bundle TG of G. In this paper, we induce a left invariant contravariant pseudo-Riemannian metric on the tangent bundle TG, and we express in different cases the contravariant Levi-Civita connection and curvature of TG in terms of the contravariant Levi-Civita connection and the curvature of G. We prove that the space of differential forms Ω*(G) on G is a differential graded Poisson algebra if, and only if, Ω*(TG) is a differen

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31

PITEA, ARIANA. "A GEOMETRIC STUDY OF SOME EQUATIONS OF MATHEMATICAL PHYSICS." International Journal of Geometric Methods in Modern Physics 09, no. 04 (2012): 1250030. http://dx.doi.org/10.1142/s0219887812500302.

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We introduce geometric structures (connections, pseudo-Riemannian metrics) adapted to some fundamental problems of Differential Geometry, and find geometrical characteristics associated to equations of Mathematical Physics. Also, we introduce a geometric study of some boundary problems. Throughout this work, as main tool we employed an adequate Riemannian Hessian structure, suggested in [Int. J. Geom. Meth. Mod. Phys.7(7) (2010) 1104–1113].

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32

ṢAHIN, BAYRAM. "SEMI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS." International Journal of Geometric Methods in Modern Physics 08, no. 07 (2011): 1439–54. http://dx.doi.org/10.1142/s0219887811005725.

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This paper has two aims. First, we show that the usual notion of umbilical maps between Riemannian manifolds does not work for Riemannian maps. Then we introduce a new notion of umbilical Riemannian maps between Riemannian manifolds and give a method on how to construct examples of umbilical Riemannian maps. In the second part, as a generalization of CR-submanifolds, holomorphic submersions, anti-invariant submersions, invariant Riemannian maps and anti-invariant Riemannian maps, we introduce semi-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples

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33

Ho, Pei-Ming. "Riemannian Geometry on Quantum Spaces." International Journal of Modern Physics A 12, no. 05 (1997): 923–43. http://dx.doi.org/10.1142/s0217751x97000694.

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An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space.

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34

Siddiqui, Aliya Naaz, and Fatemah Mofarreh. "A DDVV Conjecture for Riemannian Maps." Symmetry 16, no. 8 (2024): 1029. http://dx.doi.org/10.3390/sym16081029.

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The Wintgen inequality is a significant result in the field of differential geometry, specifically related to the study of submanifolds in Riemannian manifolds. It was discovered by Pierre Wintgen. In the present work, we deal with the Riemannian maps between Riemannian manifolds that serve as a superb method for comparing the geometric structures of the source and target manifolds. This article is the first to explore a well-known conjecture, called DDVV inequality (a conjecture for Wintgen inequality on Riemannian submanifolds in real space forms proven by P.J. De Smet, F. Dillen, L. Verstra

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35

BAŞARIR NOYAN, Esra, and Yılmaz GÜNDÜZALP. "Quasi hemi-slant pseudo-Riemannian submersions in para-complex geometry." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72, no. 4 (2023): 959–75. http://dx.doi.org/10.31801/cfsuasmas.1089389.

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We introduce a new class of pseudo-Riemannian submersions which are called quasi hemi-slant pseudo-Riemannian submersions from para-Kaehler manifolds to pseudo-Riemannian manifolds as a natural generalization of slant submersions, semi-invariant submersions, semi-slant submersions and hemislant Riemannian submersions in our study. Also, we give non-trivial examples of such submersions. Further, some geometric properties with two types of quasi hemi-slant pseudo-Riemannian submersions are investigated

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36

Stoica, Ovidiu Cristinel. "The geometry of warped product singularities." International Journal of Geometric Methods in Modern Physics 14, no. 02 (2017): 1750024. http://dx.doi.org/10.1142/s0219887817500244.

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In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian man

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37

Lefevre, Jeanne, Florent Bouchard, Salem Said, Nicolas Le Bihan, and Jonathan H. Manton. "On Riemannian and non-Riemannian Optimisation, and Optimisation Geometry." IFAC-PapersOnLine 54, no. 9 (2021): 578–83. http://dx.doi.org/10.1016/j.ifacol.2021.06.119.

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38

Blaga, Adara M. "Geometry of Manifolds and Applications." Mathematics 13, no. 6 (2025): 990. https://doi.org/10.3390/math13060990.

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This editorial presents 24 research articles published in the Special Issue entitled Geometry of Manifolds and Applications of the MDPI Mathematics journal, which covers a wide range of topics from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in many branches of theoretical and applied mathematical studies, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as complex space forms, metallic Riemannian space forms, Hessian manifolds of constant Hessian curvature; optimal inequalities

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39

Park, JuneYoung, YuMi Lee, Tae-Joon Kim, and Jang-Hwan Choi. "Riemannian Geometric-based Meta Learning." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 19 (2025): 19839–47. https://doi.org/10.1609/aaai.v39i19.34185.

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Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to capture complex learning dynamics, particularly in few-shot learning scenarios. To address this limitation, we propose Stiefel-MAML, which integrates Riemannian geometry by optimizing within the Stiefel manifold, a space that naturally enforces orthogonality constraints. By leveraging the geometric structure of the Stiefel manifold, we improve parameter expr

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40

Cruceru, Calin, Gary Becigneul, and Octavian-Eugen Ganea. "Computationally Tractable Riemannian Manifolds for Graph Embeddings." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 7133–41. http://dx.doi.org/10.1609/aaai.v35i8.16877.

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Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases (e.g., hierarchical structures benefit from hyperbolic geometry). However, going beyond embedding spaces of constant sectional curvature, while potentially more representationally powerful, proves to be challenging as one can easily lose the appeal of computationally tractable tools such as geodesic distances or Riemannian gradients. Here, we explore two computationally efficient matrix manifolds, showcasing how

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41

Dr Manju Bala. "Singularities and Metric Structures in Sub-Riemannian Geometries with Applications to Control Theory." International Journal of Scientific Research in Science, Engineering and Technology 12, no. 3 (2025): 359–63. https://doi.org/10.32628/ijsrset251248.

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Sub-Riemannian geometry extends classical Riemannian frameworks by defining metrics only on constrained directions within manifolds, naturally modeling systems with nonholonomic constraints. This paper investigates the nature and impact of singularities—points where the geometric structure or metric degenerates—on the local and global properties of sub-Riemannian manifolds. We analyze metric behavior near singularities through nilpotent approximations and study their influence on geodesic existence, uniqueness, and stability, with particular emphasis on abnormal geodesics. Further, we explore

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42

MASTROLIA, PAOLO, MARCO RIGOLI, and MICHELE RIMOLDI. "SOME GEOMETRIC ANALYSIS ON GENERIC RICCI SOLITONS." Communications in Contemporary Mathematics 15, no. 03 (2013): 1250058. http://dx.doi.org/10.1142/s0219199712500587.

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43

Carfora, Mauro, and Francesca Familiari. "Ricci curvature and quantum geometry." International Journal of Geometric Methods in Modern Physics 17, no. 04 (2020): 2050049. http://dx.doi.org/10.1142/s0219887820500498.

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We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum) fluctuations around a background fiducial geometry. In such a scenario, Ricci curvature with its subtle connections to diffusion, optimal transport, Wasserestein geometry and renormalization group, features prominently.

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44

Nazimuddin, AKM, and Md Showkat Ali. "Riemannian Geometry and Modern Developments." GANIT: Journal of Bangladesh Mathematical Society 39 (November 19, 2019): 71–85. http://dx.doi.org/10.3329/ganit.v39i0.44159.

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In this paper, we compute the Christoffel Symbols of the first kind, Christoffel Symbols of the second kind, Geodesics, Riemann Christoffel tensor, Ricci tensor and Scalar curvature from a metric which plays a fundamental role in the Riemannian geometry and modern differential geometry, where we consider MATLAB as a software tool for this implementation method. Also we have shown that, locally, any Riemannian 3-dimensional metric can be deformed along a directioninto another metricthat is conformal to a metric of constant curvature GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 71-85

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45

Boscain, Ugo, Remco Duits, Francesco Rossi, and Yuri Sachkov. "Curve cuspless reconstructionviasub-Riemannian geometry." ESAIM: Control, Optimisation and Calculus of Variations 20, no. 3 (2014): 748–70. http://dx.doi.org/10.1051/cocv/2013082.

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46

Hitchin, Nigel. "Integral systems in Riemannian geometry." Surveys in Differential Geometry 4, no. 1 (1998): 21–81. http://dx.doi.org/10.4310/sdg.1998.v4.n1.a1.

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47

Wolf, Michael. "TEICHMÜLLER THEORY IN RIEMANNIAN GEOMETRY." Bulletin of the London Mathematical Society 26, no. 3 (1994): 315–16. http://dx.doi.org/10.1112/blms/26.3.315.

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48

Bejancu, Aurel. "Curvature in sub-Riemannian geometry." Journal of Mathematical Physics 53, no. 2 (2012): 023513. http://dx.doi.org/10.1063/1.3684957.

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49

Chen, Bang-Yen. "RIEMANNIAN GEOMETRY OF LAGRANGIAN SUBMANIFOLDS." Taiwanese Journal of Mathematics 5, no. 4 (2001): 681–723. http://dx.doi.org/10.11650/twjm/1500574989.

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50

Beggs, Edwin, and Shahn Majid. "Nonassociative Riemannian geometry by twisting." Journal of Physics: Conference Series 254 (November 1, 2010): 012002. http://dx.doi.org/10.1088/1742-6596/254/1/012002.

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