On (α, β, γ)-metrics

2020/11/22 by Sadeghzadeh, Nasrin, Rajabi, Tahere
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.12778

Abstract

In this paper, a new class of Finsler metrics which are included (α,β)-metrics are introduced. They are defined by a Riemannian metric and two 1-forms β=b_i(x)yⁱ and γ= γ_i(x)yⁱ. This class of metrics are a generalization of (α,β)-metrics which are not always (α,β)-metric. We find a necessary and sufficient condition for this metric to be locally projectively flat and then we prove the conditions for this metric to be of Douglas type.

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