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# On a Yamabe Type Problem in Finsler Geometry

Published:2017-03-02
Printed: Jun 2017
• Bin Chen,
Department of Mathematics, Tongji University, Shanghai, China, 200092
• Lili Zhao,
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China, 200240
 Format: LaTeX MathJax PDF

## Abstract

In this paper, a new notion of scalar curvature for a Finsler metric $F$ is introduced, and two conformal invariants $Y(M,F)$ and $C(M,F)$ are defined. We prove that there exists a Finsler metric with constant scalar curvature in the conformal class of $F$ if the Cartan torsion of $F$ is sufficiently small and $Y(M,F)C(M,F)\lt Y(\mathbb{S}^n)$ where $Y(\mathbb{S}^n)$ is the Yamabe constant of the standard sphere.
 Keywords: Finsler metric, scalar curvature, Yamabe problem
 MSC Classifications: 53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20] 58B20 - Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]

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