On birecurrent affine motions in a Finsler manifold
type: Item
instance of: scholarly article
title: On birecurrent affine motions in a Finsler manifold
zbMATH Open document ID: 0576.53019
DOI: 10.1007/BF01957019
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: Affine motions generated by recurrent and birecurrent vector fields in a non-Riemannian manifold of recurrent curvature were studied by \textit{K. Takano} [Tensor, New Ser. 11, 161-173, 245-253 (1961; Zbl 0099.376)] and by \textit{K. Takano} and \textit{T. Imai} [ibid. 23, 309-313 (1972; Zbl 0259.53019)]. In the present paper the author finds a necessary and sufficient condition for a birecurrent vector field to generate an affine motion in a general Finsler manifold and from this condition deduces the same condition for a recurrent vector field. The author also finds the integrability condition. Finally, the affine motions generated by the above vector fields in some special Finsler manifolds are studied.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 3921405
zbMATH Keywords: birecurrent vector fields
zbMATH Keywords: affine motion
zbMATH Keywords: recurrent vector field
zbMATH Keywords: Finsler manifolds
author: P. N. Pandey
reviewed by: F. C. Klepp
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3921405