Immersions into spheres with parallel higher fundamental forms
type: Item
instance of: scholarly article
title: Immersions into spheres with parallel higher fundamental forms
zbMATH Open document ID: 0859.53045
author: Antonella Carfagna D'Andrea
published in: Beiträge zur Algebra und Geometrie
publication date: 1997-04-14T00:00:00Z
full work available at URL: https://eudml.org/doc/222537
full work available at URL: no.1
review text: In this note the author proves that the minimal immersions of a compact rank one symmetric space into a unit \(n\)-sphere with higher fundamental forms isotropic have all higher fundamental forms parallel, so they are 2-symmetric submanifolds of the unit \(n\)-sphere. As a consequence, helical minimal geodesic immersions into spheres and standard minimal immersions into spheres are examples of 2-symmetric submanifolds. The author also gives conditions under which a nicely-curved 2-symmetric submanifold of a space of constant curvature \(c\geq 0\) is a helical immersion and vice versa.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 928010
zbMATH Keywords: minimal immersions
zbMATH Keywords: compact rank one symmetric space
zbMATH Keywords: submanifolds of the unit \(n\)-sphere
zbMATH Keywords: 2-symmetric submanifolds
zbMATH Keywords: helical immersion
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 928010