具有共形广义径向场的球对称Finsler流形

On spherically symmetric Finsler manifolds with conformal generalized radial fields

共形向量场在Finsler几何的研究特别是共形航海问题中起着重要的作用.本文通过建立和求解相应的偏微分方程,完全确定以广义径向场为共形向量场的所有球对称Finsler度量.这些度量包含常截面曲率的Riemann度量.

Conformal vector fields play an important role in the study of Finsler geometry,especially in the conformal navigation problem.In this paper,by establishing and solving the corresponding partial differential equations,we determine all spherically symmetric Finsler metrics with generalized radial fields as conformal vector fields completely.These Finsler metrics include Riemannian metrics of constant sectional curvature.