Harmonic Gauss maps
type: Item
instance of: scholarly article
title: Harmonic Gauss maps
zbMATH Open document ID: 0643.53040
author: Gary R. Jensen
author: M. Rigoli
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A construction is given whereby a Riemannian manifold induces a Riemannian metric on the total space of a large class of fibre bundles over it. Using this metric on the appropriate bundles, necessary and sufficient conditions are given for the Gauss map and the spherical Gauss map to be harmonic. A weak maximum principle is applied to the Gauss map of an isometric immersion into Euclidean space in order to prove a sufficient condition for when such an immersion with parallel mean curvature vector must be minimal.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 4048576
zbMATH Keywords: Riemannian metric
zbMATH Keywords: fibre bundles
zbMATH Keywords: Gauss map
zbMATH Keywords: weak maximum principle
zbMATH Keywords: parallel mean curvature vector
zbMATH Keywords: harmonic map
zbMATH Keywords: minimal immersion
MaRDI profile type: Publication
full work available at URL: pjm.1989.136.261
OpenAlex ID: W2014027391
DOI: 10.2140/PJM.1989.136.261
description: scientific article; zbMATH DE number 4048576