Finsler spaces with Riemannian geodesics
Abstract
In Finsler spaces the intervalds=F(x i ,dx i ) is an arbitrary function of the coordinatesx i and coordinate incrementsdx i withF homogeneous of degree one in thedx i . It is shown that for Riemannian spacesds R 2=g ij dx i dx i which admit a non trivial covariantly constant tensorH i .(x k ) there is an associated Finsler space with the same geodesic structure. The subset of such Finsler spaces withH i .(x k ) a vector or second rank decomposable tensor is determined.
- Publication:
-
General Relativity and Gravitation
- Pub Date:
- September 1991
- DOI:
- 10.1007/BF00756867
- Bibcode:
- 1991GReGr..23.1071R