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Geometric interpretation of curvature and torsion tensors in a generalized Finsler space

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We give geometric interpretations of a torsion tensor and curvature tensors in a generalized Finsler space (with an asymmetric basic tensor).

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References

  1. S. M. Minčić and M. Lj. Zlatanović, “New Commutation Formulas for δ-Differentation in Generalized Finsler Space,” Differ.Geom. Dyn. Syst. 12, 145–157 (2010).

    MathSciNet  MATH  Google Scholar 

  2. M. Lj. Zlatanović and S. M. Minčić, “Identities for Curvature Tensors inGeneralized Finsler Space,” Filomat 23(2), 34–42 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Rund, The Differential Geometry of Finsler Spaces (Springer, 1959).

  4. S. M. Minčić and M. Lj. Zlatanović, “Derived Curvature Tensors in Generalized Finsler Space,” Differ. Geom. Dyn. Syst. 13, 179–190 (2011).

    MathSciNet  MATH  Google Scholar 

  5. S. I. Vacaru, “Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics on Nonholonomic Manifolds,” arXiv:0806.3810v1 [gr-qc] 24 Jun 2008.

  6. M. I. Wanas, “An AP-Structure with Finslerian Flavor: I,” Modern Physics Letters A 24(22), 1749–1762 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. I. Yoshihoro, L. Il-Yong, and P. Hong-Suh, “On Generalized Finsler Space Structure with a Vanishing hv-Torsion,” J. KoreanMath. Soc. 41(2), 369–378 (2004).

    Google Scholar 

  8. N. L. Youssef and Amr M. Sid-Ahmed, “Linear Connections and Curvature Tensors in the Geometry of Parallelizable Manifolds,” ReportsMath. Physics, 60(1), 39–53 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Lj. Zlatanović and S. M. Minčić, “Bianchi Type Identities in Generalized Finsler Space,” Hypercomplex numbers in geometry and physics 7(2), 109–118 (2010).

    Google Scholar 

  10. F. Graif, “Sulla Posibilita di Construire Parallelogrami Chiusi in Alcune Varieta a Torsione,” Boll. d. Un. math. Ital., Ser. III, 7, 132–135 (1952).

  11. E. Cartan, Les Espaces de Finsler (Paris, 1934).

  12. A. Einstein, “Bianchi Identities in the Generalized Theory of Gravitation,” Canad. J. Math. 2(2), 120–128, 1950.

    Article  MATH  Google Scholar 

  13. A. Einstein, “Relativistic Theory of the Non-symmetric Field,” Appendix II in the book: The Meaning of Relativity (5th Ed., Princeton, 49, 1955).

  14. A. Einstein, “Generalization of the Relativistic Theory of Gravitation,” Ann. math. (2), Princeton, 46(4), 576–584 (1945).

    Google Scholar 

  15. L. P. Eisenhart, “Generalized Riemann Spaces,” Proc. Nat. Acad. Sci. USA 37(5), 311–315 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  16. S. M. Minčić, “Geometric Interpretations of Curvature Tensors and Pseudotensors of the Spaces with Nonsymmetric Affine Connection,” Publ. Inst.Math., Beograd, 47(61), 113–120 (1990).

    MathSciNet  Google Scholar 

  17. M. Prvanović, “Four Curvature Tensors of Asymmetric Affine Connection,” in 150 Years of Lobachevskii Geometry (Kazan, 1976, Moscow, 1977), pp. 199–205.

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Correspondence to S. M. Minčić.

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Original Russian Text © S.M. Minčić and M.L. Zlatanović, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 1, pp. 31–40.

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Minčić, S.M., Zlatanović, M.L. Geometric interpretation of curvature and torsion tensors in a generalized Finsler space. Russ Math. 57, 26–34 (2013). https://doi.org/10.3103/S1066369X13010039

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  • DOI: https://doi.org/10.3103/S1066369X13010039

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