호남수학학술지 (Honam Mathematical Journal)

  • 제46권2호
  • /
  • Pages.198-208
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  • 2024
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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INVARIANT (α, β)-METRIC OF DOUGLAS AND BERWALD TYPE

  • Kirandeep Kaur (Department of Mathematics, Punjabi University College, Ghudda, (Constituent College of Punjabi University Patiala)) ;
  • Gauree Shanker (Department of Mathematics & Statistics, School of Basic Sciences, Central University of Punjab)
  • 투고 : 2023.06.20
  • 심사 : 2023.10.07
  • 발행 : 2024.06.25
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초록

In this paper, we find the conditions for a homogeneous Finsler space with an invariant infinite series (α, β)-metric to be of Berwald type. Also, we derive the necessary and sufficient condition for such a metric to be a Douglas metric.

키워드

과제정보

The second author is thankful to DST Gov. of India for providing financial support in terms of DST-FST label-I grant vide sanction number SR/FST/MSI/2021/104(C).

참고문헌

  1. P. L. Antonelli, R. S. Ingarden, and M. Matsumoto, The Theory of Sprays and Finsler spaces with Applications in Physics and Biology, Kluwer Academic Publishers, Netherlands, 1993.
  2. A. Arvanitoyeorgos, An Introduction to Lie groups and the Geometry of Homogeneous Spaces, Vol. 22, American Mathematical Soc., 2003.
  3. S. Bacso and M. Matsumoto, On Finsler spaces of Douglas type. A generalization of the notion of Berwald space, Publ. Math. Debrecen 51 (1997), 385-406.
  4. D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer-Verlag, New York, 2000.
  5. X. Chen and Z. Shen, On Douglas metrics, Publ. Math. Debrecen 66 (2005), 503-512.
  6. S. S. Chern, Finsler geometry is just Riemannian geometry without the quadratic restriction, Notices Amer. Math. Soc. 43 (1996), no. 9, 959-963.
  7. S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics, Vol. 6, World Scientific Publishers, 2005.
  8. S. Deng and Z. Hou, The group of isometries of a Finsler space, Pacific J. Math. 207 (2002), 149-155.
  9. S. Deng and Z. Hu, Curvatures of homogeneous Randers spaces, Adv. Math. 240 (2013), 194-226.
  10. J. Douglas, The general geometry of paths, Ann. of Math. 29 (1927-28), 143-168.
  11. K. Kaur and G. Shanker, Ricci curvature of a homogeneous Finsler space with exponential metric, DGDS 22 (2020), 130-140.
  12. K. Kaur and G. Shanker, Flag curvature of a naturally reductive homogeneous Finsler space with infinite series metric, Appl. Sci. 22 (2020), 114-127.
  13. K. Kaur and G. Shanker, On the geodesics of a homogeneous Finsler space with a special (α, β)-metric, J. Finsler Geom. and Its Appl. 1 (2020), no. 1, 26-36.
  14. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience Publishers, Vol. 1, 1963; Vol. 2, 1969.
  15. B. Li, Y. Shen, and Z. Shen, On a class of Douglas metrics, Studia Sci. Math. Hungar. 46 (2009), 355-365.
  16. H. Liu and S. Deng, Homogeneous (α, β)-metrics of Douglas type, Forum Math. 27 (2015), 3149-3165.
  17. M. Matsumoto, On a C-reducible Finsler space, Tensor N. S. 24 (1972), 29-37.
  18. M. Matsumoto, The Berwald connection of a Finsler space with an (α, β)-metric, Tensor N. S. 50 (1991), 18-21.
  19. K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33-65.
  20. G. Randers,On an asymmetric metric in the four-space of general relativity, Phys. Rev. 59 (1941), 195-199.
  21. G. Shanker and K. Kaur, Naturally reductive homogeneous space with an invariant (α, β)-metric, Lobachevskii J. Math. 40 (2019), no. 2, 210-218.
  22. G. Shanker and K. Kaur, Homogeneous Finsler space with infinite series (α, β)-metric, Appl. Sci. 21 (2019), 219-235.
  23. G. Shanker and K. Kaur, Homogeneous Finsler space with exponential metric, Adv. Geom. 20 (2020), no. 3, 391-400.
  24. Z. I. Szabo, Positive definite Berwald spaces : Structure theorems on Berwald spaces, Tensor N. S. 35 (1981), 25-39.
  25. G. Yang, On a class of two-dimensional Douglas and projectively flat Finsler metrics, Sci. World J. 2013, Article ID 291491, 11 pages.