Left Invariant Finsler Manifolds are Generalized Berwald


  • 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


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


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.






Differential Geometry

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