Left Invariant Finsler Manifolds are Generalized Berwald

Bernadett Aradi

Abstract

In this note we show that a Lie group endowed with a left invariant Finsler function is a generalized Berwald manifold. This observation makes it possible to construct a whole class of generalized Berwald manifolds, thus satisfying a request of Hashiguchi [6]: `... find much more interesting examples'. In particular, we show that the Randers Lie group constructed by Libing and Mo [9] is in fact a proper generalized Berwald manifold. We also have a look at the more specific bi-invariant case, and review some essential results concerning bi-invariant Finsler functions with (at least partly) new and conceptual proofs.

Keywords

generalized Berwald manifold, Lie group, left invariant Finsler function, averaging process, geodesics

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