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On a Yamabe Type Problem in Finsler Geometry
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2017
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