Some Properties of the <i>χ</i>-Curvature under Conformal Transformation

Abstract

In this paper, we identify the sufficient and necessary conditions for conformally related Randers metrics to have the same χ-curvature. Further, if s0=0 holds, we conclude that the conformal transformation must be a homothety. Using the divergence theorem, we prove that, on the compact manifold, there is no nontrivial conformal transformation preserving the χ-curvature of the Randers metrics invariant.

Keywords

• <b>χ</b>-curvature
• conformal transformations
• randers metrics