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arXiv · 1706.00533

On Landsberg general $(α,β)$-metrics with a conformal 1-form

Shasha Zhou·Benling Li
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Abstract

In this paper, we study almost regular Landsberg general $(α,β)$-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we give the classification of Landsberg general $(α,β)$-metrics under the conditon that $β$ is closed and conformal to $α$. Under this condition, we prove that regular Landsberg general $(α,β)$-metrics must be Berwaldian when the dimension is greater than two. For the almost regular case, the classification also is given and some new non-Berwaldian Landsberg metrics are found.

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Shasha Zhou, Benling Li. 2017-06-02. On Landsberg general $(α,β)$-metrics with a conformal 1-form. https://arxiv.org/abs/1706.00533

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