On a class of projectively flat (α,β) metrics

Articles in Press

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

Given any Finsler metric F on a smooth manifold, its symmetrized metric Fˆ(x,y):=1/2(F(x,y)+F(x,-y) may inherit some geometric properties of F. We examine this fact for the Matsumoto metric F=α2/(α-β) and prove that if the Matsumoto metric is locally projectively flat then, so is its symmetrized metric Fˆ=α3/(α2-β2). In particular, the converse result also holds.

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References

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Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 08 May 2026

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