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Results in Mathematics

, 74:21 | Cite as

On m-Kropina Finsler Metrics of Scalar Flag Curvature

  • Guojun YangEmail author
Article
  • 17 Downloads

Abstract

In this paper, we consider a special class of singular Finsler metrics: m-Kropina metrics which are defined by a Riemannian metric and a 1-form. We show that an m-Kropina metric (\(m\ne -1\)) of scalar flag curvature must be locally Minkowskian in dimension \(n\ge 3\). We characterize by some PDEs a Kropina metric (\(m=-1\)) which is respectively of scalar flag curvature and locally projectively flat in dimension \(n\ge 3\), and obtain some principles and approaches of constructing non-trivial examples of Kropina metrics of scalar flag curvature.

Keywords

m-Kropina metric flag curvature projective flatness 

Mathematics Subject Classification

53B40 53A20 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China

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