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arXiv · 1303.6263

Chern connection of a pseudo-Finsler metric as a family of affine connections

Miguel Angel Javaloyes
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Abstract

We consider the Chern connection of a (conic) pseudo-Finsler manifold $(M,L)$ as a linear connection $\nabla^V$ on any open subset $\Omega\subset M$ associated to any vector field $V$ on $\Omega$ which is non-zero everywhere. This connection is torsion-free and almost metric compatible with respect to the fundamental tensor $g$. Then we show some properties of the curvature tensor $R^V$ associated to $\nabla^V$ and in particular we prove that the Jacobi operator of $R^V$ along a geodesic coincides with the one given by the Chern curvature.

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Miguel Angel Javaloyes. 2013-03-25. Chern connection of a pseudo-Finsler metric as a family of affine connections. https://arxiv.org/abs/1303.6263

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