Isometric immersions with homothetical Gauss map
type: Item
instance of: scholarly article
title: Isometric immersions with homothetical Gauss map
zbMATH Open document ID: 0702.53033
DOI: 10.1007/BF00181689
author: Stefan Nölker
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: The author classifies the isometric immersions f: \(M\to {\mathbb{R}}^ n\) from a simply connected, totally complete Riemannian manifold (M,g) into \({\mathbb{R}}^ n\) with flat normal bundle, a) for which the third fundamental form is a constant multiple of the Riemannian metric g, and b) whose third fundamental form is parallel. If f belongs to the class b), then it is a product of immersions of the class a); and if f belongs to the class a), then it is a product of standard embeddings of spheres and of special curves. The results follow from a careful investigation of the principal curvature distributions.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 4151290
zbMATH Keywords: Gauss map
zbMATH Keywords: isometric immersions
zbMATH Keywords: third fundamental form
zbMATH Keywords: product of immersions
reviewed by: Helmut Reckziegel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181689
OpenAlex ID: W1964481317
description: scientific article; zbMATH DE number 4151290