Congruence of minimal surfaces and higher fundamental forms
type: Item
instance of: scholarly article
title: Congruence of minimal surfaces and higher fundamental forms
zbMATH Open document ID: 1030.53011
author: T. Vlachos
published in: Manuscripta Mathematica
publication date: 2003-03-27T00:00:00Z
review text: The author proves that minimal surfaces in space forms are determined, up to ambient isometries, by the Hopf differentials and the induced metric. Hopf differentials in this context are higher order invariants which generalize the well known Hopf differential. In order to prove the main result the author makes use of the \(r\)th curvature ellipses (which have also been used in the study of Willmore surfaces).
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1889222
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Hopf differentials
zbMATH Keywords: space forms
zbMATH Keywords: curvature ellipses
reviewed by: Ivan C. Sterling
MaRDI profile type: Publication
full work available at URL: s00229-002-0310-z
OpenAlex ID: W2047123387
Wikidata QID: Q125357832
DOI: 10.1007/S00229-002-0310-Z
description: scientific article; zbMATH DE number 1889222