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On a Yamabe Type Problem in Finsler Geometry

Published online by Cambridge University Press:  20 November 2018

Bin Chen  and
Lili Zhao
Bin Chen
Affiliation:
Department of Mathematics, Tongji University, Shanghai, China, 200092. e-mail: chenbin@tongji.edu.cn
Lili Zhao
Affiliation:
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China, 200240. e-mail: zhaolili@sjtu.edu.cn
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Abstract

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In this paper, a newnotion 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 $Y(M,F)C(M,F)<Y({{\mathbb{S}}^{n}})$ where $Y({{\mathbb{S}}^{n}})$ is the Yamabe constant of the standard sphere.

Keywords

53C6058B20Finsler metricscalar curvatureYamabe problem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 253 - 268
Copyright
Copyright © Canadian Mathematical Society 2017

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