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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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