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Search: MSC category 58B20 ( Riemannian, Finsler and other geometric structures [See also 53C20, 53C60] )

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Chen, Bin; Zhao, Lili
 On a Yamabe type problem in Finsler geometry 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 problemCategories:53C60, 58B20
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