Projectively flat general (α,β)-metrics with constant flag curvature

2015/02/05 by Changtao Yu, Yu, Changtao, Hongmei Zhu +1
Physics and Astronomy · #53B40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1502.01395

openalex publication_date 2015/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the flag curvature of a particular class of Finsler metrics called general (α,β)-metrics, which are defined by a Riemannian metric α and a 1-form β. The classification of such metrics with constant flag curvature are completely determined under some suitable conditions, which make them be locally projectively flat. As a result, we construct some new projectively flat Finsler metrics with flag curvature 1, 0 and -1, all of which are of singularity at some directions.

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