Isotropic minimal submanifolds in a space form
type: Item
instance of: scholarly article
title: Isotropic minimal submanifolds in a space form
zbMATH Open document ID: 0659.53045
author: Takehiro Itoh
published in: Tsukuba Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The author proves the following: Let M be an n-dimensional compact minimal submanifold immersed in a sphere of curvature c. If M is isotropic and the sectional curvature K of M satisfies \(nc/3(n+2)\leq K\leq c,\) then \(K\equiv c\) (i.e., M is totally geodesic) or \(K\equiv nc/2(n+1)\) (i.e., M is a Veronese submanifold of degree 2) or \(K\equiv nc/3(n+2)\) (i.e. is a Veronese submanifold of degree 3).
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4078196
zbMATH Keywords: minimal submanifold
zbMATH Keywords: sphere
zbMATH Keywords: sectional curvature
zbMATH Keywords: totally geodesic
zbMATH Keywords: Veronese submanifold
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160846
OpenAlex ID: W2618909580
DOI: 10.21099/TKBJM/1496160846
description: scientific article; zbMATH DE number 4078196