On Finsler geometry of submanifolds
type: Item
instance of: scholarly article
title: On Finsler geometry of submanifolds
zbMATH Open document ID: 0921.53037
published in: Mathematische Annalen
publication date: 1999-09-26T00:00:00Z
review text: The main purpose of this paper is to show that the geometry of Finsler submanifolds can be investigated without the theory of Finsler connections. First, by using the Cartan tensor field, the author finds a Finsler manifold which cannot be immersed in any finite-dimensional Minkowski space. Then he defines the mean curvature and the normal curvature of a Finsler immersion. Finally, he proves some global results on closed oriented submanifolds of a Minkowski space. We think that the method introduced by the author of the present paper might have the potential to clarify the huge amount of questions from the geometry of Finsler submanifolds.
reviewed by: Aurel Bejancu
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1195758
zbMATH Keywords: mean curvature
zbMATH Keywords: normal curvature
zbMATH Keywords: Minkowski space
zbMATH Keywords: Finsler submanifolds
author: Zhongmin Shen
MaRDI profile type: Publication
full work available at URL: s002080050200
OpenAlex ID: W2036365068
DOI: 10.1007/S002080050200
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description: scientific article; zbMATH DE number 1195758