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On m-Kropina Finsler Metrics of Scalar Flag Curvature

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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.

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  1. Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

    Guojun Yang

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  1. Guojun Yang
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Correspondence to Guojun Yang.

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Supported by the National Natural Science Foundation of China (11471226).

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Yang, G. On m-Kropina Finsler Metrics of Scalar Flag Curvature. Results Math 74, 21 (2019). https://doi.org/10.1007/s00025-018-0946-y

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  • DOI: https://doi.org/10.1007/s00025-018-0946-y

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