arXiv Open Access 2013

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

Miguel Angel Javaloyes

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Abstrak

We consider the Chern connection of a (conic) pseudo-Finsler manifold $(M,L)$ as a linear connection $\nabla^V$ on any open subset $Ω\subset M$ associated to any vector field $V$ on $Ω$ 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.

Topik & Kata Kunci

math.DG

Penulis (1)

Miguel Angel Javaloyes

Format Sitasi

APA MLA BibTeX

Javaloyes, M.A. (2013). Chern connection of a pseudo-Finsler metric as a family of affine connections. https://arxiv.org/abs/1303.6263

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2013
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓