Minimal immersions of 2-manifolds into spheres
type: Item
instance of: scholarly article
title: Minimal immersions of 2-manifolds into spheres
zbMATH Open document ID: 0543.53045
DOI: 10.1007/BF01174890
author: Michael Kozlowski
author: Udo Simon
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173452
review text: The following theorem is proved. Let \(M^ 2\) be a compact, connected, two-dimensional Riemannian manifold with curvature K. Assume that 1/6\(\leq K\leq 1/3\), and let \(x:M^ 2\to S^ N(1)\) be an isometric minimal immersion into the unit N-sphere. Then either \(K=1/3\) or \(K=1/6\), and the immersions are the standard minimal immersions corresponding to the spherical harmonics of order 2 and 3. The proof depends on finding a suitable integral formula.
reviewed by: Manfredo P. do Carmo
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 3864042
zbMATH Keywords: curvature pinching
zbMATH Keywords: minimal immersion
zbMATH Keywords: spherical harmonics
zbMATH Keywords: integral formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3864042