Journal articles: 'Riemannian symmetric spaces'

1

Jimenez, J. A. "Riemannian 4-Symmetric Spaces." Transactions of the American Mathematical Society 306, no. 2 (April 1988): 715. http://dx.doi.org/10.2307/2000819.

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Jim{énez, J. A. "Riemannian $4$-symmetric spaces." Transactions of the American Mathematical Society 306, no. 2 (February 1, 1988): 715. http://dx.doi.org/10.1090/s0002-9947-1988-0933314-6.

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Berezovski, Volodymyr, Yevhen Cherevko, and Lenka Rýparová. "Conformal and Geodesic Mappings onto Some Special Spaces." Mathematics 7, no. 8 (July 25, 2019): 664. http://dx.doi.org/10.3390/math7080664.

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In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

4

Burstall, Francis, Simone Gutt, and John Rawnsley. "Twistor spaces for Riemannian symmetric spaces." Mathematische Annalen 295, no. 1 (January 1993): 729–43. http://dx.doi.org/10.1007/bf01444914.

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Petrović, Miloš Z., Mića S. Stanković, and Patrik Peška. "On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces." Mathematics 7, no. 7 (July 15, 2019): 626. http://dx.doi.org/10.3390/math7070626.

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We consider conformal and concircular mappings of Eisenhart’s generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart’s generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart’s generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.

6

Chen, Bang-Yen, and Lieven Vanhecke. "Reflections and symmetries in compact symmetric spaces." Bulletin of the Australian Mathematical Society 38, no. 3 (December 1988): 377–86. http://dx.doi.org/10.1017/s000497270002774x.

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Point symmetries and reflections are two important transformations on a Riemannian manifold. In this article we study the interactions between point symmetries and reflections in a compact symmetric space when the reflections are global isometries.

7

Chu, Cho-Ho. "JORDAN SYMMETRIC SPACES." Asian-European Journal of Mathematics 02, no. 03 (September 2009): 407–15. http://dx.doi.org/10.1142/s1793557109000339.

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We introduce a class of Riemannian symmetric spaces, called Jordan symmetric spaces, which correspond to real Jordan triple systems and may be infinite dimensional. This class includes the symmetric R-spaces as well as the Hermitian symmetric spaces.

8

Kiosak, Volodymyr, Olexandr Lesechko, and Olexandr Latysh. "On geodesic mappings of symmetric pairs." Proceedings of the International Geometry Center 15, no. 3-4 (March 4, 2023): 230–38. http://dx.doi.org/10.15673/tmgc.v15i3-4.2430.

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The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.

9

Mashimo, Katsuya, and Koji Tojo. "Circles in Riemannian symmetric spaces." Kodai Mathematical Journal 22, no. 1 (1999): 1–14. http://dx.doi.org/10.2996/kmj/1138043984.

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Binh, T. Q. "On weakly symmetric Riemannian spaces." Publicationes Mathematicae Debrecen 42, no. 1-2 (January 1, 1993): 103–7. http://dx.doi.org/10.5486/pmd.1993.1281.

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De, U. C., and Somnath Bandyopadhyay. "On weakly symmetric Riemannian spaces." Publicationes Mathematicae Debrecen 54, no. 3-4 (April 1, 1999): 377–81. http://dx.doi.org/10.5486/pmd.1999.1999.

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12

Kiosak, V., L. Kusik, and V. Isaiev. "Geodesic Ricci-symmetric pseudo-Riemannian spaces." Proceedings of the International Geometry Center 15, no. 2 (September 30, 2022): 109–19. http://dx.doi.org/10.15673/tmgc.v15i2.2224.

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We introduced special pseudo-Riemannian spaces, called geodesic A-symmetric spaces, into consideration. It is proven that there are no geodesic symmetric spaces and no geodesic Ricci symmetric spaces, which differ from spaces of constant curvature and Einstein spaces respectively. The research is carried out locally, by tensor methods, without any limitations imposed on a metric and a sign.

13

Berndt, Jürgen, and Carlos Olmos. "On the index of symmetric spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 737 (April 1, 2018): 33–48. http://dx.doi.org/10.1515/crelle-2015-0060.

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AbstractLetMbe an irreducible Riemannian symmetric space. The index ofMis the minimal codimension of a (nontrivial) totally geodesic submanifold ofM. We prove that the index is bounded from below by the rank of the symmetric space. We also classify the irreducible Riemannian symmetric spaces whose index is less than or equal to 3.

14

Biswas, Indranil, and Niels Leth Gammelgaard. "Vassiliev invariants from symmetric spaces." Journal of Knot Theory and Its Ramifications 25, no. 10 (September 2016): 1650055. http://dx.doi.org/10.1142/s0218216516500553.

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We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are exactly characterized by having the symmetries of the Riemann curvature tensor.

15

SZŐKE, RÓBERT. "COMPLEX CROWNS OF SYMMETRIC SPACES." International Journal of Mathematics 16, no. 08 (September 2005): 889–902. http://dx.doi.org/10.1142/s0129167x05003156.

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16

Chongshan, Luo. "On concircular transformations in Riemannian spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 2 (April 1986): 218–25. http://dx.doi.org/10.1017/s1446788700027191.

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AbstractThis paper introduces a tensor that contains the Riemannian curvature tensor and the conformal curvature tensor as special examples in the Riemannian space (Mn, g), and by using this tensor we define C-semi-symmetric space. In this paper, we have the following main result: if there is a non-trivial concircular transformation between two C-semi-symmetric spaces, then both spaces are of quasi-constant curvature.

17

Falbel, Elisha, and Claudio Gorodski. "On contact sub-riemannian symmetric spaces." Annales scientifiques de l'École normale supérieure 28, no. 5 (1995): 571–89. http://dx.doi.org/10.24033/asens.1726.

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18

Hassani, A. "Wave equation on Riemannian symmetric spaces." Journal of Mathematical Physics 52, no. 4 (April 2011): 043514. http://dx.doi.org/10.1063/1.3567167.

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19

Cornea, Emil, Hongtu Zhu, Peter Kim, and Joseph G. Ibrahim. "Regression models on Riemannian symmetric spaces." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79, no. 2 (March 20, 2016): 463–82. http://dx.doi.org/10.1111/rssb.12169.

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20

Bougerol, Philippe, and Thierry Jeulin. "Brownian bridge on Riemannian symmetric spaces." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 333, no. 8 (October 2001): 785–90. http://dx.doi.org/10.1016/s0764-4442(01)02145-0.

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21

Szőke, Róbert. "Quantization of compact Riemannian symmetric spaces." Journal of Geometry and Physics 119 (September 2017): 286–303. http://dx.doi.org/10.1016/j.geomphys.2017.05.008.

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22

'Olafsson, G., and H. Schlichtkrull. "Wave propagation on Riemannian symmetric spaces." Journal of Functional Analysis 107, no. 2 (August 1992): 270–78. http://dx.doi.org/10.1016/0022-1236(92)90107-t.

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23

Chu, Cho-Ho. "Jordan triples and Riemannian symmetric spaces." Advances in Mathematics 219, no. 6 (December 2008): 2029–57. http://dx.doi.org/10.1016/j.aim.2008.08.001.

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24

Branson, T., G. �lafsson, and H. Schlichtkrull. "Hyghens' principle in Riemannian symmetric spaces." Mathematische Annalen 301, no. 1 (January 1995): 445–62. http://dx.doi.org/10.1007/bf01446638.

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25

Kowalski, Oldřich, and Lieven Vanhecke. "Classification of five-dimensional naturally reductive spaces." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 3 (May 1985): 445–63. http://dx.doi.org/10.1017/s0305004100063027.

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Naturally reductive homogeneous spaces have been studied by a number of authors as a natural generalization of Riemannian symmetric spaces. A general theory with many examples was well-developed by D'Atri and Ziller[3]. D'Atri and Nickerson have proved that all naturally reductive spaces are spaces with volume-preserving local geodesic symmetries (see [1] and [2]).

26

LE, HUILING, and DENNIS BARDEN. "ON SIMPLEX SHAPE SPACES." Journal of the London Mathematical Society 64, no. 2 (October 2001): 501–12. http://dx.doi.org/10.1112/s0024610701002332.

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The right-invariant Riemannian metric on simplex shape spaces in fact makes them particular Riemannian symmetric spaces of non-compact type. In the paper, the general properties of such symmetric spaces are made explicit for simplex shape spaces. In particular, a global matrix coordinate representation is suggested, with respect to which several geometric features, important for shape analysis, have simple and easily computable expressions. As a typical application, it is shown how to locate the Fréchet means of a class of probability measures on the simplex shape spaces, a result analogous to that for Kendall's shape spaces.

27

Liang, Ke, and Quanqin Jin. "Minimal symmetric submani folds in compact Riemannian symmetric spaces." Chinese Science Bulletin 43, no. 21 (November 1998): 1786–89. http://dx.doi.org/10.1007/bf02883372.

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28

Andreeva, Tatiana A., Dmitry N. Oskorbin, and Evgeny D. Rodionov. "Investigation of conformally killing vector fields on 5-dimensional 2-symmetric lorentzian manifolds." Yugra State University Bulletin 60, no. 1 (December 23, 2021): 17–22. http://dx.doi.org/10.17816/byusu20210117-22.

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Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investigated in cases k=2,3 by D.V. Alekseevsky, A.S. Galaev and others. For arbitrary k, non-trivial examples of such spaces are known: generalized Kachen - Wallach manifolds. In the case of small dimensions, these spaces and Killing vector fields on them were studied by D.N. Oskorbin, E.D. Rodionov, and I.V. Ernst with the helpof systems of computer mathematics. In this paper, using the Sagemath SCM, we investigate conformally Killing vector fields on five-dimensional indecomposable 2- symmetric Lorentzian manifolds, and construct an algorithm for their computation.

29

Gindikin, Simon, and Bernhard Krötz. "Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces." Transactions of the American Mathematical Society 354, no. 8 (April 3, 2002): 3299–327. http://dx.doi.org/10.1090/s0002-9947-02-03012-x.

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30

Berezovskii, V. E., I. Hinterleitner, N. I. Guseva, and J. Mikeš. "Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces." Mathematical Notes 103, no. 1-2 (January 2018): 304–7. http://dx.doi.org/10.1134/s0001434618010315.

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31

Федченко, Юлія Степанівна, and Олександр Васильович Лесечко. "Special semi-reducible pseudo-Riemannian spaces." Proceedings of the International Geometry Center 14, no. 1 (April 16, 2021): 48–59. http://dx.doi.org/10.15673/tmgc.v14i1.1940.

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The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent. The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces. The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces. The research is carried out locally in tensor shape, without limitations imposed on a sign of a metric.

32

Dõng, Trần Đạo. "A compact imbedding of Riemannian Symmetric Spaces." Hue University Journal of Science: Natural Science 127, no. 1A (June 20, 2018): 55. http://dx.doi.org/10.26459/hueuni-jns.v127i1a.4825.

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Let G be a connected real semisimple Lie group with finite center and θ be a Cartan involution of G. Suppose that K is the maximal compact subgroup of G corresponding to the Cartan involution θ. The coset space X = G/K is then a Riemannian symmetric space. In this paper, by choosing the reduced root system Σ0 = {α ∈ Σ | 2α /∈ Σ; α 2 ∈/ Σ} insteads of the restricted root system Σ and using the action of the Weyl group, firstly we construct a compact real analytic manifold Xb 0 in which the Riemannian symmetric space G/K is realized as an open subset and that G acts analytically on it, then we consider the real analytic structure of Xb 0 induced from the real analytic srtucture of AbIR, the compactification of the corresponding vectorial part.

33

Inoguchi, Jun-ichi, and Toru Sasahara. "Biharmonic hypersurfaces in Riemannian symmetric spaces I." Hiroshima Mathematical Journal 46, no. 1 (March 2016): 97–121. http://dx.doi.org/10.32917/hmj/1459525933.

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34

NILSSON, Andreas. "Fourier multipliers on non-Riemannian symmetric spaces." Journal of the Mathematical Society of Japan 57, no. 1 (January 2005): 295–308. http://dx.doi.org/10.2969/jmsj/1160745826.

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35

Inoguchi, Jun-ichi, and Toru Sasahara. "Biharmonic hypersurfaces in Riemannian symmetric spaces II." Hiroshima Mathematical Journal 47, no. 3 (November 2017): 349–78. http://dx.doi.org/10.32917/hmj/1509674451.

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36

Sarkar, Rudra P., and Jyoti Sengupta. "Beurling's theorem for Riemannian symmetric spaces II." Proceedings of the American Mathematical Society 136, no. 05 (December 5, 2007): 1841–54. http://dx.doi.org/10.1090/s0002-9939-07-08990-3.

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37

Marinosci, R. A. "Generalized pointwise symmetric Riemannian spaces: a classification." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 3 (November 1988): 505–20. http://dx.doi.org/10.1017/s0305004100065695.

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The theory of generalized symmetric spaces was begun by P. J. Graham and A. J. Ledger in 1967 in their paper [1]. Other authors who contributed to this topic were, e.g. F. Brickel, A. Deicke, A. S. Fedenko, A. Gray, V. G. Kac, M. Obata, B. Pettit, K. Sekigawa and J. Wolf; more recently also J. A. Jiménez, A. R. Razawi, C. Sánchez, M. Sekizawa, M. Toomanian, G. Tsagas and L. Vanhecke. A systematic exposition is given in the book by O. Kowalski[3, 4]. The author classifies all generalized symmetric Riemannian spaces in dimension n ≤ 5, using a systematic method.

38

Dušek, Zdeněk, and Oldřich Kowalski. "Pseudo-Riemannian manifolds modelled on symmetric spaces." Monatshefte für Mathematik 165, no. 3-4 (July 20, 2010): 319–26. http://dx.doi.org/10.1007/s00605-010-0234-8.

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39

Mikesh, I., and V. S. Sobchuk. "Geodesic mappings of 3-symmetric Riemannian spaces." Journal of Mathematical Sciences 69, no. 1 (March 1994): 885–87. http://dx.doi.org/10.1007/bf01250819.

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40

Ólafsson, Gestur, and Angela Pasquale. "Ramanujanʼs Master Theorem for Riemannian symmetric spaces." Journal of Functional Analysis 262, no. 11 (June 2012): 4851–90. http://dx.doi.org/10.1016/j.jfa.2012.03.006.

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41

Li, Luoqing. "Riesz Means on Compact Riemannian Symmetric Spaces." Mathematische Nachrichten 168, no. 1 (November 11, 2006): 227–42. http://dx.doi.org/10.1002/mana.19941680114.

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42

Verh�czki, L. "Special isoparametric orbits in Riemannian symmetric spaces." Geometriae Dedicata 55, no. 3 (May 1995): 305–17. http://dx.doi.org/10.1007/bf01266321.

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43

BERNDT, JÜRGEN, and YOUNG JIN SUH. "HYPERSURFACES IN NONCOMPACT COMPLEX GRASSMANNIANS OF RANK TWO." International Journal of Mathematics 23, no. 10 (October 2012): 1250103. http://dx.doi.org/10.1142/s0129167x12501030.

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Consider a Riemannian manifold N equipped with an additional geometric structure, such as a Kähler structure or a quaternionic Kähler structure, and a hypersurface M in N. The geometric structure induces a decomposition of the tangent bundle TM of M into subbundles. A natural problem is to classify all hypersurfaces in N for which the second fundamental form of M preserves these subbundles. This problem is reasonably well understood for Riemannian symmetric spaces of rank one, but not for higher rank symmetric spaces. A general treatment of this problem for higher rank symmetric spaces is out of reach at present, and therefore it is desirable to understand this problem better in a few special cases. Due to some conceptual differences between symmetric spaces of compact type and of noncompact type it appears that one needs to consider these two cases separately. In this paper we investigate this problem for the rank two symmetric space SU 2, m/S(U2Um) of noncompact type.

44

Wu, Tong, and Yong Wang. "Super warped products with a semi-symmetric non-metric connection." AIMS Mathematics 7, no. 6 (2022): 10534–53. http://dx.doi.org/10.3934/math.2022587.

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<abstract><p>In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we introduce two kinds of super warped product spaces with a semi-symmetric non-metric connection and give the conditions that two super warped product spaces with a semi-symmetric non-metric connection are the Einstein super spaces with a semi-symmetric non-metric connection.</p></abstract>

45

Calvaruso, G., and L. Vanhecke. "Semi-symmetric ball-homogeneous spaces and a volume conjecture." Bulletin of the Australian Mathematical Society 57, no. 1 (February 1998): 109–15. http://dx.doi.org/10.1017/s0004972700031452.

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We prove that semi-symmetric ball-homogeneous spaces are locally symmetric and we use this result to prove that a semi-symmetric Riemannian manifold such that the volume of each sufficiently small geodesic ball is the same as in a Euclidean space, is locally flat.

46

Sarkar, Rudra P., and Jyoti Sengupta. "Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type." Canadian Mathematical Bulletin 50, no. 2 (June 1, 2007): 291–312. http://dx.doi.org/10.4153/cmb-2007-029-6.

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47

Mare, A. L., and P. Quast. "ON SOME SPACES OF MINIMAL GEODESICS IN RIEMANNIAN SYMMETRIC SPACES." Quarterly Journal of Mathematics 63, no. 3 (February 12, 2011): 681–94. http://dx.doi.org/10.1093/qmath/har003.

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48

Lesechko, O., and T. Shevchenko. "PSEUDO-RIEMANNIAN SPACES WITH A SPECIAL RIEMANN TENSOR." Mechanics And Mathematical Methods 3, no. 1 (June 2021): 106–14. http://dx.doi.org/10.31650/2618-0650-2021-3-1-106-114.

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The paper considers pseudo-Riemannian spaces, the Riemann tensor of which has a special structure. The structure of the Riemann tensor is given as a combination of special symmetric and obliquely symmetric tensors. Tensors are selected so that the results can be applied in the theory of geodetic mappings, the theory of holomorphic-projective mappings of Kähler spaces, as well as other problems arising in differential geometry and its application in general relativity, mechanics and other fields. Through the internal objects of pseudo-Riemannian space, others are determined, which are studied depending on what problems are solved in the study of pseudo-Riemannian spaces. By imposing algebraic or differential constraints on internal objects, we obtain special spaces. In particular, if constraints are imposed on the metric we will have equidistant spaces. If on the Ricci tensor, we obtain spaces that allow φ (Ric)-vector fields, and if on the Einstein tensor, we have almost Einstein spaces. The paper studies pseudo-Riemannian spaces with a special structure of the curvature tensor, which were introduced into consideration in I. Mulin paper. Note that in his work these spaces were studied only with the requirement of positive definiteness of the metric. The proposed approach to the specialization of pseudo-Riemannian spaces is interesting by combining algebraic requirements for the Riemann tensor with differential requirements for its components. In this paper, the research is conducted in tensor form, without restrictions on the sign of the metric. Depending on the structure of the Riemann tensor, there are three special types of pseudo-Riemannian spaces. The properties which, if necessary, satisfy the Richie tensors of pseudoriman space and the tensors which determine the structure of the curvature tensor are studied. In all cases, it is proved that special tensors satisfy the commutation conditions together with the Ricci tensor. The importance and usefulness of such conditions for the study of pseudo-Riemannian spaces is widely known. Obviously, the results can be extended to Einstein tensors. Proven theorems allow us to effectively investigate spaces with constraints on the Ricci tensor.

49

CALVARUSO, G., and J. VAN DER VEKEN. "LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES." International Journal of Mathematics 20, no. 10 (October 2009): 1185–205. http://dx.doi.org/10.1142/s0129167x09005728.

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We describe a global model for Lorentzian symmetric three-spaces admitting a parallel null vector field, and classify completely the surfaces with parallel second fundamental form in all Lorentzian symmetric three-spaces. Interesting differences arise with respect to the Riemannian case studied in [2]. Our results complete the classification of parallel surfaces in all three-dimensional Lorentzian homogeneous spaces.

50

Belarbi, Mansour, Hichem Elhendi, and Lakehal Belarbi. "Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces." Journal of the Indian Mathematical Society 89, no. 3-4 (August 23, 2022): 263. http://dx.doi.org/10.18311/jims/2022/29627.

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In this paper, we study biharmonic curves in three-dimensio -nal generalized symmetric spaces, equipped with a left-invariant pseudo- Riemannian metric. We characterize non-geodesic biharmonic curves in three-dimensional generalized symmetric spaces and prove that there ex- ists no non-geodesic biharmonic spacelike helix in three-dimensional gen- eralized symmetric spaces. We also show that a linear map from a Eu- clidean space in three-dimensional generalized symmetric spaces is bihar- monic if and only if it is a harmonic map, and give a complete classification of such maps.

Journal articles on the topic 'Riemannian symmetric spaces'

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