Immersed hypersurfaces with constant Weingarten curvature
type: Item
instance of: scholarly article
title: Immersed hypersurfaces with constant Weingarten curvature
zbMATH Open document ID: 0643.53043
DOI: 10.1007/BF01446438
author: Klaus Ecker
author: Gerhard Huisken
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164511
review text: We prove that isometric hypersurface immersions of non-negative sectional curvature into a spaceform are isoparametric with at most two distinct principal curvatures, provided a certain concave symmetric function f of the principal curvatures is constant. Particular examples are the cases where f is a generalized mean curvature function or a harmonic means function of the principal curvatures.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 4048579
zbMATH Keywords: non-negative sectional curvature
zbMATH Keywords: principal curvatures
zbMATH Keywords: generalized mean curvature function
zbMATH Keywords: harmonic means function
zbMATH Keywords: isoparametric hypersurface
MaRDI profile type: Publication
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OpenAlex ID: W2062227254
description: scientific article; zbMATH DE number 4048579