Curvature computations in Finsler Geometry using a distinguished class of anisotropic connections
Differential Geometry
2020-06-26 v2
Abstract
We show how to compute tensor derivatives and curvature tensors using affine connections. This allows for all computations to be obtained without using coordinate systems, in a way that parallels the computations appearing in classical Riemannian Geometry. In particular, we obtain Bianchi identities for the curvature tensor of any anisotropic connection, we compare the curvature tensors of any two anisotropic connections, and we find a family of anisotropic connections which are well suited to study the geometry of Finsler metrics.
Keywords
Cite
@article{arxiv.1904.07178,
title = {Curvature computations in Finsler Geometry using a distinguished class of anisotropic connections},
author = {Miguel Ángel Javaloyes},
journal= {arXiv preprint arXiv:1904.07178},
year = {2020}
}
Comments
19 pages; v2: title changed, added Remark 3.7 and some further explanations along the paper