Non-existence of certain types of NP-Finsler spaces
type: Item
instance of: scholarly article
title: Non-existence of certain types of NP-Finsler spaces
zbMATH Open document ID: 0626.53018
DOI: 10.1007/BF01903366
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: A projective Finsler space \(F_ n\) satisfying the relation \(\nabla_{\ell}N^ h_{ijk}=\lambda_{\ell}N^ h_{ijk}\) (resp. \(\nabla_{\ell}N^ h_{ijk}=0)\) for a non-vanishing covariant vector field \(\lambda_{\ell}(x)\), where \(\nabla\) is the operator of covariant differentiation with respect to the normal projective connection \(\Pi^ i_{jk}(x,\dot x)\) of \(F_ n\) with \(N^ h_{ijk}\) is the corresponding curvature tensor with respect to \(\Pi^ i_{jk}\), is called a recurrent (resp. symmetric) normal projective Finsler space, denoted by \(RNP\)-F\({}_ n\) (resp. \(SNP\)-F\({}_ n)\) [see \textit{R. B. Misra} and \textit{F. M. Meher}, Tensor, New Ser. 22, 117-120 (1971; Zbl 0206.509); the reviewer, Mat. Vesn. 10(25), 105-110 (1973; Zbl 0268.53009)]. In this paper, the author calls such a Finsler space for which Berwald's connection coefficients \(G^ i_{jk}\) also satisfy \(G^ i_{jkr}=0\) trivial normal projective Finsler space, and shows that a non-trivial RNP- (resp. SNP-) Finsler space \(F_ n\) \((n>2)\) does not exist.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 4017793
zbMATH Keywords: Finsler space
zbMATH Keywords: trivial normal projective Finsler space
author: P. N. Pandey
reviewed by: Om Prakash Singh
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01903366
OpenAlex ID: W2097134292
description: scientific article; zbMATH DE number 4017793