The splitting and deformations of the generalized Gauss map of compact CMC surfaces
type: Item
instance of: scholarly article
title: The splitting and deformations of the generalized Gauss map of compact CMC surfaces
zbMATH Open document ID: 0959.53036
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2001-05-02T00:00:00Z
review text: The study of constant mean curvature surfaces in the 3-sphere, which are often called CMC surfaces, has a long and interesting development and it continues to attract the attention of differential geometers. In the paper under review, the author proves that the generalized Gauss map of CMC surfaces in the 3-sphere globally splits into two non-conformal harmonic maps into the 2-sphere. As a corollary of this result, it is proved that a full superconformal minimal surface in \(S^{4m}\) cannot be isometric to a minimal surface in the 3-sphere \(S^3\), which gives a partial answer to Lawson's conjecture.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1321872
zbMATH Keywords: harmonic map
zbMATH Keywords: constant mean curvature
zbMATH Keywords: generalized Gauss map
zbMATH Keywords: minimal surface
zbMATH Keywords: Lawson's conjecture
author: Reiko Miyaoka
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178224851
OpenAlex ID: W2078814549
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DOI: 10.2748/TMJ/1178224851
description: scientific article; zbMATH DE number 1321872