A GEOMETRIC CHARACTERIZATION OF FINSLER MANIFOLDS OF CONSTANT CURVATURE K = 1

A. BEJANCU ； H. R. FARRAN

《International Journal of Mathematics and Mathematical Sciences》 2000卷 (2000/12) Pp. 399-407-048

https://doi.org/10.1155/S0161171200002179

摘要

We prove that a Finsler manifold F^m is of constant curvature K = 1 if and only if the unit horizontal Liouville vector field is a Killing vector field on the indicatrix bundle IM of F^m.

關鍵字

Finsler manifold of constant curvature ； Killing vector field ； indicatrix bundle ； horizontal Liouville vector field