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arXiv · 1110.5680

On the Berwald-Landsberg problem

Ricardo Gallego Torrome
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Abstract

Given a Finsler space (M,F), one can define natural average Riemannian metrics on M by averaging on the indicatrix I_x the fundamental tensor g of the Finsler function $F$. In this paper we determine explicitly the Levi-Civita connection for these average Riemannian metrics. We apply the result to the case when (M,F) is a Landsberg space. Using a particular averaging procedure, the invariance of the average metric along a homotopy in the space of Finsler structures over M is shown. As a consequence of such invariance, we prove that any C^5 regular Landsberg space is a Berwald space.

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Ricardo Gallego Torrome. 2015-05-18. On the Berwald-Landsberg problem. https://arxiv.org/abs/1110.5680

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