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

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1. CMB 2017 (vol 60 pp. 253)

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 problem
Categories:53C60, 58B20

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