Nonlinear connections in a Finsler space
type: Item
instance of: scholarly article
title: Nonlinear connections in a Finsler space
zbMATH Open document ID: 0673.53017
DOI: 10.1007/BF01951569
author: S. C. Rastogi
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: On a Finsler space \(F_ n\) connections \(\Gamma^{1}{}^ i_ k(x,X)\) and \(\Gamma^{2}_{jk}(x,Y)\) nonlinear in the vectors \(X^ i(x)\) resp. \(Y_ j(x)\) are considered and the torsion tensors \(\Omega^{1}_ j{}^ i_ k:=\Gamma^{1}_ j{}^ i_ k-\Gamma^{1}_ k{}^ i_ j,\) \(\Gamma^{1}_ j{}^ i_ k\equiv \frac{\partial}{\partial X^ j}\Gamma^{1}{}^ i_ k\); \(\Omega^{2}_ j{}^ i_ h:=\Gamma^{2}_ j{}^ i_ h-\Gamma^{2}_ h{}^ i_ j,\) \(\Gamma^{2}_ j{}^ i_ h\equiv \frac{\partial}{\partial Y_ i}\Gamma^{2}_{j\;k}\) are studied. It is shown that if geodesics are auto-parallel curves, then \(\Omega^{2}_ j{}^ i_ k=0.\) Also ex-central connections and semi-symmetric connections are investigated under the condition that geodesics are auto-parallel curves.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 4102015
zbMATH Keywords: Finsler space
zbMATH Keywords: ex-central connections
zbMATH Keywords: semi-symmetric connections
zbMATH Keywords: geodesics
zbMATH Keywords: auto-parallel curves
reviewed by: Lajos Tamássy
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01951569
OpenAlex ID: W2068773573
description: scientific article; zbMATH DE number 4102015