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arXiv · 1404.3488

The Landsberg equation of a Finsler space

Ming Xu·Shaoqiang Deng
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Abstract

Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observation that the solution space is invariant under the linear isometries of the tangent Minkowski spaces, we prove that an $(α_1, α_2)$-metric of the Landsberg type must be a Berwald metric. This shows that the hunting for a unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful even in the very broad class of $(α_1,α_2)$-metrics.

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Ming Xu, Shaoqiang Deng. 2014-04-14. The Landsberg equation of a Finsler space. https://arxiv.org/abs/1404.3488

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