Projective Changes Between the Polynomial (α, β)-metric and the Generalized Kropina Metric
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we look at the projective relativity of (α, β)-metrics. Let α and ¯α be Riemannian metrics, and β and β¯ be non-zero one-forms on a manifold M of dimension at least 2. We give necessary and sufficient conditions for an (α, β)-metric F and an (¯α, β¯)-metric F¯ to be projectively related. In particular this gives conditions for the polynomial (α, β)-metric and a generalized Kropina (¯α, β¯)-metric to be projectively related. We then investigate these conditions in more detail when F is assigned special curvature properties.
Abstract
In this paper, we look at the projective relativity of (α, β)-metrics. Let α and ¯α be Riemannian metrics, and β and β¯ be non-zero one-forms on a manifold M of dimension at least 2. We give necessary and sufficient conditions for an (α, β)-metric F and an (¯α, β¯)-metric F¯ to be projectively related. In particular this gives conditions for the polynomial (α, β)-metric and a generalized Kropina (¯α, β¯)-metric to be projectively related. We then investigate these conditions in more detail when F is assigned special curvature properties.
참고문헌 (22)
- P. L. Antonelli, "The theory of sprays and Finsler spaces with applications in Physics and Biology" (2013), Springer
- S. Basco, "Projective change between Finsler spaces with (α, β)-metric", Tensor (N. S.), 55, pp.252~257 (1994)
- S. S. Chern, "Riemann-Finsler Geometry", Nankai Tracts Math., 23 (2005)
- N. Cui, "On the S-curvature of some (α, β)-metrics", Acta Math. Sci., 26A(7), pp.1047~1056 (2006)
- N. Cui, "Projective change between two classes of (α, β)-metric", Differential Geom. Appl., 27, pp.566~573 (2009)
- G. Hall, "Geodesics and the geometry of manifolds", Balkan J. Geom. Appl., 19(1), pp.54~61 (2014)
- V. K. Kropina, "On projective Finsler spaces with a certain special form, Naucn", Doklady vyss. Skoly, fiz.-mat. Nauki, 1959(2), pp.38~42 (1960)
- P. Kumar, "Projective Changes between Generalized (α, β)-Metric and Randers Metric", Adv. Pure Math., 10(5), pp.312~321 (2020)
- M. Matsumoto, "A slope of a mountain is a Finsler surface with respect to time measure", J. Math. Kyoto Univ., 29, pp.17~25 (1989)
- M. Matsumoto, "Theory of Finsler spaces with (α, β)-metric", Rep. Math. Phys., 31, pp.43~83 (1992)
- M. Matsumoto, "Finsler spaces with (α, β)-metric of Douglas type", Tensor(N. S. ), 60, pp.123~134 (1998)
- F. Mu, "On the projective equivalence between (α, β)-metrics and Kropina metrics", Differ. Geom. Dyn. Syst., 14, pp.105~116 (2012)
- H. S. Park, "Projective changes between a Finsler space with (α, β)-metric and the associated Riemannian metric", Tensor (N. S.), 24, pp.163~188 (1984)
- H. S. Park, "On projectively flat Finsler spaces with (α, β)-metric", Commun. Korean Math. Soc., 14, pp.373~383 (1999)
- H. S. Park, "The Randers changes of Finsler spaces with (α, β)-metrics of Douglas type", J. Korean Math. Soc., 38(3), pp.503~521 (2001)
- A. Rapscak, "Uber die bahntreuen Abbildungen metrisher Raume", Publ. Math. Debrecen, 8, pp.1071~1089 (1961)
- G. Shanker, "Nonholonomic frame for Finsler spaces with a special quartic metric", Indian J. pure appl. Math., 120(2), pp.283~290 (2018)
- Z. Shen, "On projectively related Einstein metrics in Riemann-Finsler geometry", Math. Ann., 320, pp.625~647 (2001)
- Z. Shen, "On Einstein Square metrics", Publ. Math. Debrecen, 85(3-4), pp.413~424 (2014)
- B. Tiwari, "On the projective change between two special Finsler space of (α, β)-metrics", An. Stiint. Univ. Al. I. Cuza lasi Mat. (N. S.), 3(2), pp.891~900 (2016)
- G. P. Yadav, "Projective Change Between Randers Metric And Exponential (α, β)-Metric", Facta Univ. Ser. Math. Inform, 33(3), pp.389~399 (2018)
- M. Zohrehvand, "On projectively related of two special classes of (α, β) metrics", Differential Geom. Appl., 29(5), pp.660~669 (2011)