On the Berwald-Landsberg problem

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.

This paper has been withdraw by the author due to a crucial error in the last section of the paper

References in corpus (3)

• Finsleroid--Finsler Space with Berwald and Landsberg Conditions
• Finsleroid--Finsler Space and Spray Coefficients
• On a rigidity condition for Berwald Spaces

Cited by in corpus (1)

• An equivalence theorem of a class of Minkowski norms and its applications