International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 6, Pages 399-407
doi:10.1155/S0161171200002179
A Geometric characterization of Finsler manifolds of constant
curvature K=1
Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait
Received 7 December 1998
Copyright © 2000 A. Bejancu and H. R. Farran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that a Finsler manifold 𝔽m 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
𝔽m.