Constant mean curvature surfaces in 4-space forms
type: Item
instance of: scholarly article
title: Constant mean curvature surfaces in 4-space forms
zbMATH Open document ID: 0652.53003
author: J.-H. Eschenburg
author: Renato de Azevedo Tribuzy
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108094
review text: The authors study existence and uniqueness for isometric immersions between a fixed simply connected Riemannian surface and a fixed 4- dimensional space form of curvature c, which have a parallel mean curvature vector. A typical theorem: There exists such an immersion with \(H>0\), if and only if \(K\leq c+H\) 2, and the function \(a=(c+H\) \(2- K)^{1/2}\) is of absolute value type with \(\Delta\) log a\(=2K\). Up to local congruences, all these form a two parameter family.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4063951
zbMATH Keywords: isothermal coordinates
zbMATH Keywords: isometric immersions
zbMATH Keywords: Riemannian surface
zbMATH Keywords: parallel mean curvature vector
reviewed by: Dirk Ferus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4063951