Deformations and Hilbert's Fourth Problem

2012/09/05 by Yu, Changtao · 1 citation
#53B40 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1209.0845

Abstract

In this paper we study a class of Finsler metrics defined by a Riemannian metric and an 1-form. We classify those of projectively flat in dimension n≥3 by a special class of deformations. The results show that the projective flatness of such kind of Finsler metrics always arises from that of some Riemannian metric.

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• Deformations and Einstein metrics I

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