On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature

Abstract

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(\alpha ,\beta )$-metrics which are locally projectively flat with constant flag curvature in dimension $n=2$ and $n\ge 3$ respectively. Further, we determine the local structure of $m$-Kropina metrics and particularly Kropina metrics which are projectively flat with constant flag curvature and prove that such metrics must be locally Minkowskian but are not necessarily flat-parallel.

14 pages

References in corpus (2)

• On a Class of Two-Dimensional Singular Douglas and Projectively flat Finsler Metrics
• On a Class of Singular Douglas and Projectively flat Finsler Metrics

Cited by in corpus (2)

• On a Class of Two-Dimensional Singular Douglas and Projectively flat Finsler Metrics
• On a Class of Singular Douglas and Projectively flat Finsler Metrics