Champ de vecteurs projectifs sur le fibré unitaire. (Projective vector field on unitary fibre bundle)
type: Item
instance of: scholarly article
title: Champ de vecteurs projectifs sur le fibré unitaire. (Projective vector field on unitary fibre bundle)
zbMATH Open document ID: 0582.53027
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1986-01-01T00:00:00Z
review text: We give a characterization of a projective vector field on Finslerian unitary fibre bundle and we prove that, in the compact case, the existence of projective vectors is related to the sign of the sectional curvature. We define the notion of projective restricted infinitesimal transformations. A new projectively invariant tensor is introduced, we determine necessary and sufficient conditions of nullities of projective invariants. We study the case when the mean directional curvature (M.D.C.) is satisfied under certain conditions, especially when the curvature is constant (that is a generalization of Einstein's space). We demonstrate that, any Finsler manifold, of M.D.C. positive constant, simply connected, metrically complete, and admitting a proper projective vector field, leaving invariant the covector trace of torsion, is homeomorphic to an n-sphere. We shall consider the case of a manifold with Euclidean connection.
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 3931934
zbMATH Keywords: projective vector field
zbMATH Keywords: Finslerian unitary fibre bundle
zbMATH Keywords: projective restricted infinitesimal transformations
zbMATH Keywords: mean directional curvature
zbMATH Keywords: Finsler manifold
author: Hassan Akbar-Zadeh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3931934