The Geometry of Spherically Symmetric Finsler Manifolds

Speaker: Xiaohuan Mo, Peking University.

Date: 17 aug 2018, 14h.

Place: Room 409, Bloco H, Campus Gragoatá, UFF.

Abstract:  In this lecture we discuss geometry of spherically symmetric Finsler manifolds. We describe non-trivial examples of spherically symmetric Finsler metrics satisfying different curvature conditions. We review recent results in differential geometry with spherically symmetric Finsler metrics. In particular, we find a sufficient and necessary condition for a spherically symmetric Finsler metric to be a GDW-metric. As its application, we show that a certain class of spherically symmetric Finsler metrics with are Douglas metrics if they are GDW-metrics, generalized a theorem previously only known in the case of Weyl metrics.