Academic report of Professor MoXiaoHuan of Peking University

2020-12-01  拓扑与几何组 Hits:[]

time: 2020.12.8,14:30-15:30pm

place:Tencent meeting 308 161 001

lecturer:Professor MoXiaoHuan

topic:Homogeneous Einstein Finsler metrics on $(4n+3)$-dimensional spheres

abstract:In this lecture,we discuss 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 $1$ among 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.

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