On Generalized Randers Manifolds

Details On Generalized Randers Manifolds On Generalized Randers Manifolds

2006-07-22

arxiv.org/abs/math/0607572v1

Alg.Groups Geom. 16 (1999) 115-126

Mathematics

Differential Geometry

10 pages, LaTeX file

Scientific paper

By a Randers' structure on a manifold $M$ we mean a Finsler structure $L^*=L+\alpha$, where $L$ is a Riemannian structure and $\alpha$ is a 1-form on $M$. This structure was first introduced by Randers ~\cite{[8]} from the standpoint of general relativity. In this paper, we replace $L$ by a Finsler structure, calling the resulting manifold a generalized Randers manifold. On one hand, we develop in some depth generalized Randers manifolds. On the other hand, we apply the results obtained in a foregoing paper ~\cite{[12]} to generalized Randers manifolds to obtain some new results in that domain. Among many results, we establish a necessary and sufficient condition for a generalized Randers manifold to be a general Landsberg manifold. It should be noticed that our approach is in general a global one.

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