On conformal transformation of Ξ-curvature

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Urmia University, West Azarbayjan, Iran

2 Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

Abstract

In this paper, we study the conformal transformation of recent defined non-Riemannian curvature in Finsler Geometry, namely Ξ-curvature. Indeed, we obtain the necessary and sufficient condition under which the conformal transformation preserves the Ξ-curvature.

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[1] T. Aikou, Locally conformal Berwald spaces and Weyl structures, Publ. Math. Debrecen, 49 (1996), pp. 113–
126.
[2] S. Bacs ´ o and X. Cheng ´ , Finsler conformal transformations and the curvature invariances, Publ. Math.
Debrecen, 70 (2007), pp. 221–231.
[3] G. Chen, Q. He, and Z. Shen, On conformally flat (α, β)-metrics with constant flag curvature, Publ. Math.
Debrecen, 86 (2015), pp. 387–400.
[4] M. Hashiguchi, On conformal transformations of Finsler metrics, J. Math. Kyoto Univ., 16 (1976), pp. 25–50.
[5] L. Kang, On conformally flat Randers metrics, Sci. Sin., Math., 41 (2011), pp. 439–446.
[6] M. S. Knebelman, Conformal geometry of generalized metric spaces., Proc. Natl. Acad. Sci. USA, 15 (1929),
pp. 376–379.
[7] M. Matsumoto, Conformally Berwald and conformally flat Finsler spaces, Publ. Math. Debrecen, 58 (2001),
pp. 275–285.
[8] Z. Shen, On some non-Riemannian quantities in Finsler geometry, Canad. Math. Bull., 56 (2013), pp. 184–
193.
[9] A. Tayebi and M. Razgordani, On conformally flat fourth root (α, β)-metrics, Differential Geom. Appl.,
62 (2019), pp. 253–266.
[10] C. Vincze, On the existence of C-conformal changes of Riemann-Finsler metrics, Tsukuba J. Math., 24 (2000),
pp. 419–426.
[11] C. Vincze, On a scale function for testing the conformality of a Finsler manifold to a Berwald manifold, J.
Geom. Phys., 54 (2005), pp. 454–475.