On Conformal Kropina Transformation of m-TH Root Metrics
Authors
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Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura - 281406
Manoj Kumar -
Department of Mathematics and Statistics, Dr. Ram Manohar Lohiya Awadh University, Faizabad - 224201C. K. Mishra
DOI:
https://doi.org/10.18311/jims/2021/26632Keywords:
Finsler space, conformal transformation, Kropina metrics, m-th root metrics, locally projectively flatAbstract
In this paper, we consider conformal Kropina transformation of m-th root metric and for this find Fundamental metric tensors and Spray coefficients. Moreover, condition for locally projectively flat on conformal Kropina transformation of m-th root metric has been found.
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References
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, The Netherlands, 58, 1993.
G. S. Asanov, Finslerian Extension of General Relativity, Reidel, Dordrecht, 1984.
V. Balan, Notable submanifolds in Berwald-Mo´or spaces, BSG Proc. 17, Geometry Balkan Press, (2010), 21-30.
V. Balan and N. Brinzei, Einstein equations for (h, v)− Berwald-Mo´or relativistic models, Balkan. J. Geom. Appl., 11 (2) (2006), 20–26.
M. Hashiguchi, On conformal transformation of Finsler metrics, J. Math. Kyoto University, 16 (1976), 25–50.
B. Li and Z. Shen, Projectively flat fourth root Finsler metrics, Canad. Math. Bulletin, 55 (2012), 138–145.
M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Saikawa, Otsu, Japan, 1986.
Z. Shen and S. S. Chern, Riemann-Finsler Geometry, Nankai Tracts in Mathematics, World Scientific, 6 (2004).
H. Shimada, On Finsler spaces with the metric m√ai1...imyi1...yim, Tensor, N. S., 33 (1979), 365–372.
A. Tayebi and B. Najafi, On m-th root Finsler metrics, J. Geometry and Physics, 61 (2011), 1479-1484.
A. Tayebi, T. Tabatabaeifar and E. Peyghan, On Kropina change for m-th root Finsler metrics, Ukrainian Math. J., 66 (1) (2014).
Y. Yu and Y. Yu, On Einstein m-th root metrics, Differential Geom. Appl., 28 (2010), 290–294.
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