On some $ m $-th root metrics-Reference-Cited by-同舟云学术

On some $ m $-th root metrics

Published:2024 Issue:9 Volume:9 Page:23971-23978
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zhang Xiaoling¹,Ma Cuiling¹,Zhao Lili²

Affiliation:

1. College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China

2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

Abstract

<p>The Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the $ m $-th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish. Further, we prove that a locally conformally flat cubic Finsler metric with weakly isotropic scalar curvature must be locally Minkowskian.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference14 articles.

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