Submanifolds in Finsler spaces of scalar-curvature
type: Item
instance of: scholarly article
title: Submanifolds in Finsler spaces of scalar-curvature
zbMATH Open document ID: 0702.53014
author: Sorin Dragomir
published in: Ricerche di Matematica
publication date: 1988-01-01T00:00:00Z
review text: The author proves the following four theorems: a. If \(M^ n\) is a totally geodesic submanifold of a Finsler space of scalar curvature, then \(M^ n\) is a Finsler space of scalar curvature, too. b. If \(M^ n\) is a totally umbilical submanifold of a Finsler space, then the mean curvature is v-parallel, where v denotes the intrinsic Finsler vector field. The induced and intrinsic connections of \(M_ n\) coincide. c. If \(M^ n\) is a totally-geodesic submanifold of a locally Minkowski space, then \(M_ n\) is a locally Minkowski space, too. d. Let \(M^ 2\) be a closed umbilical Landsberg surface in the Finsler space \(M^ 3(c)\) of positive scalar curvature. If the induced and intrinsic connection of \(M^ 2\) coincide then \(\chi (M^ 2)\neq 0\), where \(\chi (M^ 2)\) is the Euler- Poincaré characteristic of \(M^ 2\).
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4151271
zbMATH Keywords: totally geodesic submanifold
zbMATH Keywords: Finsler space
zbMATH Keywords: totally umbilical submanifold
zbMATH Keywords: locally Minkowski space
zbMATH Keywords: Landsberg surface
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4151271