Conformally Transformed Einstein Generalized m-th root with Curvature Properties

M K Roopa; S K Narasimhamurthy

doi:10.56424/jts.v11i01.10588

M K Roopa Department of P. G. Studies and Research in Mathematics, Kuvempu University, Shankaraghatta - 577451, Shivamogga, Karnataka, India
S K Narasimhamurthy Department of P. G. Studies and Research in Mathematics, Kuvempu University, Shankaraghatta - 577451, Shivamogga, Karnataka, India

DOI: https://doi.org/10.56424/jts.v11i01.10588

Keywords: Finsler space, Generalized m−th metric, conformal transformation, locally dually flat, Einstein metric, Ricci curvature and Isotropic mean Berwald curvature

Abstract

The purpose of the present paper is to study the confromal transformation of generalized m−th root Finsler metric. The spray co-effecients, Riemannian curvature and Ricci curvature of conformally transformed generalized m-th root metric are shown to be rational function of direction. Further, under certain conditions it is shown that a conformally transformed generalized m−th root metric is locally dually flat if and only if the conformal transformation is homothetic. Moreover, the condition for the conformally transformed metrics to be Einstein then, it is Ricci flat and Isotropic mean Berwald curvature are also found.