Homogeneous Einstein Finsler Metrics on -dimensional Spheres

Source abstract

Abstract In this paper, we study a class of homogeneous Finsler metrics of vanishing $S$ -curvature on a $(4n+3)$ -dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$ -curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.