Left Invariant Finsler Manifolds are Generalized Berwald

Authors

  • Bernadett Aradi MTA-DE Research Group ``Equations, Functions and Curves'', Hungarian Academy of Sciences and Institute of Mathematics, University of Debrecen, 4010-Debrecen, P.O. Box 12

Keywords:

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

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.

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Published

2015-01-29

Issue

Vol. 8 No. 1: (January 2015)

Section

Differential Geometry

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How to Cite

Left Invariant Finsler Manifolds are Generalized Berwald. (2015). European Journal of Pure and Applied Mathematics, 8(1), 118-125. https://www.ejpam.com/index.php/ejpam/article/view/2260