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On the conformal scalar curvature equations on Finsler manifolds

Department of Mathematics and Computer Science, Amirkabir University of Technology (Polytechnic of Tehran), Tehran, Iran

E-mail Address: shojaee_neda@aut.ac.ir

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and

Morteza MirMohammad Rezaii

Department of Mathematics and Computer Science, Amirkabir University of Technology (Polytechnic of Tehran), Tehran, Iran

E-mail Address: mmreza@aut.ac.ir

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https://doi.org/10.1142/S0219887817500086Cited by:0 (Source: Crossref)

Abstract

In this paper, we study conformal deformations and $C$ $C$ -conformal deformations of Ricci-directional and second type scalar curvatures on Finsler manifolds. Then we introduce the best equation to study the Yamabe problem on Finsler manifolds. Finally, we restrict conformal deformations of metrics to $C$ $C$ -conformal deformations and derive the Yamabe functional and the Yamabe flow in Finsler geometry.

Keywords:

AMSC: 53C60, 53C44

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