ON CONFORMAL TRANSFORMATION OF $\boldsymbol m$-th ROOT FINSLER METRIC

Authors

  • B. Tiwari DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi-221005, India Author
  • M. Kumar DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi-221005, India Author

Keywords:

Finsler space, $m$-th root metric, conformal transformation, locally dually flat metric, Einstein metric, Ricci curvature, isotropic mean

Subjects:

53B40, 53C60

Abstract

The purpose of the present paper is to study the conformaltransformation of $m$-th root Finsler metric. The spraycoefficients, Riemann curvature and Ricci curvature of conformallytransformed $m$-th root metrics are shown to be certain rationalfunctions of direction. Further, under certain conditions it isshown that a conformally transformed $m$-th root metric is locallydually flat if and only if the transformation is a homothety.Moreover the conditions for the transformed metrics to be Einsteinand isotropic mean Berwald curvature are also found.

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Published

2020-04-15

Issue

Vol. 72 No. 2 (2020): Vol. 72, Issue 2

Section

Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.