Kropina Metrics with Isotropic Scalar Curvature via Navigation Data

Abstract

Through an interesting physical perspective and a certain contraction of the Ricci curvature tensor in Finsler geometry, Akbar-Zadeh introduced the concept of scalar curvature for the Finsler metric. In this paper, we show that the Kropina metric is of isotropic scalar curvature if and only if F is an Einstein metric according to the navigation data. Moreover, we obtain the three-dimensional rigidity theorem for an Einstein–Kropina metric.

Keywords

• Kropina metrics
• scalar curvature
• Einstein metrics