Projective Change between Matsumoto Metric and Generalized Kropina Metric
Authors
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Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur - 304022 ,IN
Renu . -
Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur - 304022 ,INRamdayal Singh Kushwaha
DOI:
https://doi.org/10.18311/jims/2023/29104Keywords:
Finsler Metric, (α, β)-Metric, Projective Change, Douglas Metric and S-Curvature.Abstract
In the present paper, we find the conditions to characterize the projective change between Finsler spaces with (α, β)-metrics such as Matsumoto metric and generalized Kropina metric on a manifold with dimension n > 2. Moreover, we consider this Projective change when Matsumoto metric has some special curvature properties.
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Copyright (c) 2023 Renu ., Ramdayal Singh Kushwaha
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2022-07-08
Published 2023-07-12
References
P. L. Antonelli, Roman S. Ingarden, and M. Matsumoto, The theory of sprays and Finsler spaces with applications in Physics and Biology, Springer-Dordrecht, 2013.
S. B´asc´o and M. Matsumoto, Projective change between Finsler spaces with (α, β)-metric, Tensor (N. S.), 55 (1994), 252–257.
X. Cheng and C. Lu, Two Kinds of Weak Berwald Metrics of Scalar Flag Curvature, J. Math. Res. Exposition, 29 (2009), 607–614.
S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts Math., 2005.
N. Cui and Yi B. Shen, Projective change between two classes of (α, β)-metric, Differential Geom. Appl., 27 (2009), 566–573.
V. K. Kropina, On projective Finsler spaces with a certain special form, Naucn. Doklady vyss. Skoly, fiz.-mat. Nauki, 1959 (2)(1960), 38–42.
B. Li, Projective flat Matsumoto metric and its approximation, Acta Math. Sci. Ser. B Engl. Ed., 27 (2007), 781–789.
M. Matsumoto, A slope of a mountain is a Finsler surface with respect to time measure, J. Math. Kyoto Univ., 29 (1989), 17–25.
M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys., 31 (1992), 43–83.
M. Matsumoto, Finsler spaces with (α, β)-metric of Douglas type, Tensor (N. S.), 60 (1998), 123–134.
F. Mu and X. Cheng, On the projective equivalence between (α, β)-metrics and Kropina metrics, Differ. Geom. Dyn. Syst., 14 (2012), 105–116.
H. S. Park and IL Y. Lee, Projective changes between a Finsler space with (α, β)-metric and the associated Riemannian metric, Tensor (N. S.), 24 (1984), 163–188.
H. S. Park and IL Y. Lee, On projectively flat Finsler spaces with (α, β)-metric, Commun. Korean Math. Soc., 14 (1999), 373–383.
A. Rapsc´ak, Uber die bahntreuen Abbildungen metrisher R¨aume ¨ , Publ. Math. Debrecen, 8 (1961), 1071–1089.
G. Shanker and Ramdayal S. Kushwaha, Nonholonomic frame for Finsler spaces with a special quartic metric, Indian J. pure appl. Math., 120 (2)(2018), 283–290.
G. Shanker and Ruchi K. Sharma, Constant curvature conditions for generalized kropina spaces, arXiv:1810.00429v1, (2018), 1–11.
Z. Shen, On projectively related Einstein metrics in Riemann-Finsler geometry, Math. Ann., 320 (2001), 625–647.
Z. Shen and C. Yu, On Einstein Square metrics, Publ. Math. Debrecen, 85 (3-4)(2014), 413–424.
A. Tayebi and H. Sadeghi, Some (q, α, β)-metrics projectively related to a Kropina metric, G.J.A.R.C.M.G., 3 (2)(2014), 102–114.
B. Tiwari, M. Kumar, and Ghanashyam K. Prajapati, On the projective change between two special Finsler space of (α, β)-metrics, An. S¸tiint¸. Univ. Al. I. Cuza la¸si Mat. (N. S.), 3 (2)(2016), 891–900.
Ganga P. Yadav and Paras N. Pandey, Projective change between Randers metric and exponential (α, β)-metrics, Facta Univ. ser. math. inform., 33 (3)(2018), 389–399.
M. Zohrehvand and Morteza M. Rezaii, On projectively related of two special classes of (α, β) metrics, Differential Geom. Appl., 29 (5)(2011), 660–669.
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