Some Properties of the χ -Curvature under Conformal Transformation

Xiaofeng Yan, Xiaoling Zhang () and Lili Zhao
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Xiaofeng Yan: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Xiaoling Zhang: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Lili Zhao: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

Mathematics, 2023, vol. 11, issue 8, 1-19

Abstract: In this paper, we identify the sufficient and necessary conditions for conformally related Randers metrics to have the same χ -curvature. Further, if s 0 = 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: ? -curvature; conformal transformations; randers metrics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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