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Projective Change between Matsumoto Metric and Generalized Kropina Metric


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1 Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur - 304022, India
     

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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.

Keywords

Finsler Metric, (α, β)-Metric, Projective Change, Douglas Metric and S-Curvature.
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  • 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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  • Projective Change between Matsumoto Metric and Generalized Kropina Metric

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Authors

Renu
Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur - 304022, India
Ramdayal Singh Kushwaha
Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur - 304022, India

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.

Keywords


Finsler Metric, (α, β)-Metric, Projective Change, Douglas Metric and S-Curvature.

References





DOI: https://doi.org/10.18311/jims%2F2023%2F29104