Curvature computations in Finsler Geometry using a distinguished class\n of anisotropic connections

2019/04/15 by Miguel Ángel Javaloyes, Javaloyes, Miguel Ángel
Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1904.07178

openalex publication_date 2019/04/15 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We show how to compute tensor derivatives and curvature tensors using affine\nconnections. This allows for all computations to be obtained without using\ncoordinate systems, in a way that parallels the computations appearing in\nclassical Riemannian Geometry. In particular, we obtain Bianchi identities for\nthe curvature tensor of any anisotropic connection, we compare the curvature\ntensors of any two anisotropic connections, and we find a family of anisotropic\nconnections which are well suited to study the geometry of Finsler metrics.\n

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