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Deformations and Hilbert's Fourth Problem (1209.0845v1)
Published 5 Sep 2012 in math.DG and math.MG
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 $n\geq3$ 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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