Rigidity of minimal isometric immersions of spheres into spheres
type: Item
instance of: scholarly article
title: Rigidity of minimal isometric immersions of spheres into spheres
zbMATH Open document ID: 0929.53034
DOI: 10.1023/A:1005024324512
author: Christine M. Escher
published in: Geometriae Dedicata
publication date: 1999-03-22T00:00:00Z
review text: A certain minimal isometric immersion from the sphere \(S^3(1)\) to \(S^6(1/4)\), which is not totally geodesic, has been extensively studied by many authors. In this paper, the author studies uniqueness properties of this immersion proving that it is infinitesimally rigid within the class of all degree 6 minimal isometric immersions. It is also proved that it is linearly rigid; linear rigidity for minimal isometric immersions \(f\) of a manifold \(M\) into the sphere \(S^m\) is equivalent to saying that for each linear transformation \(A\) of \(\mathbb{R}^{m+1}\), the composition \(A\circ f\) is an isometric immersion.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C24
zbMATH DE Number: 1268418
zbMATH Keywords: minimal isometric immersions
zbMATH Keywords: infinitesimal rigidity
zbMATH Keywords: linear rigidity
reviewed by: M. Helena Noronha
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1268418