On projectively flat Kropina metrics

2013/04/05 by Zhang, Xiaoling, Shen, Yibing
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1304.1612

Abstract

In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric F=α²/β with constant curvature K and ‖β‖_α=1 is projectively flat if and only if F is locally Minkowskian.

Related

• On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature
• On Kropina Change of m-th Root Finsler Metrics
• On a Class of Singular Douglas and Projectively flat Finsler Metrics
• Two Families of Finsler Metrics Projectively Related to a Kropina Metric
• On a Class of Two-Dimensional Singular Douglas and Projectively flat Finsler Metrics