An estimate for the mean curvature of complete submanifolds in a tube
type: Item
instance of: scholarly article
title: An estimate for the mean curvature of complete submanifolds in a tube
zbMATH Open document ID: 0554.53037
author: Yoshihisa Kitagawa
published in: Kodai Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Let \(f: M\to N\) be an isometric immersion of an m-dimensional complete Riemannian manifold M, whose scalar curvature is bounded below, into an n-dimensional Riemannian manifold N, whose sectional curvature \(K_ N\) satisfies \(-\infty <\inf K_ N\) and \(K_ N\leq b\). For \(n>p\geq 1\), let P be a p-dimensional embedded submanifold in N and let \(TP^{\perp}\) be the normal bundle of P. We denote by \(\tau\) (P,\(\lambda)\) the tube of radius \(\lambda\) about P in N. When f(M) is contained in a tube \(\tau\) (P,\(\lambda)\) the author gives an estimate for the sup of \(| H|\), the norm of the mean curvature vector field H of the immersion f. This is a natural extension of a result due to the reviewer and \textit{D. Koutroufiotis} [Arch. Math. 40, 82-85 (1983; Zbl 0502.53042)].
reviewed by: Thomas Hasanis
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 3883155
zbMATH Keywords: scalar curvature
zbMATH Keywords: sectional curvature
zbMATH Keywords: tube
zbMATH Keywords: mean curvature vector
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138036904
OpenAlex ID: W1990927587
cites work: Q5341449
cites work: An Estimate for the Curvature of Bounded Submanifolds
cites work: A complete minimal surface in \(R^ 3\) between two parallel planes
cites work: An inequality between the exterior diameter and the mean curvature of bounded immersions
cites work: Isometric immersions of Riemannian manifolds
DOI: 10.2996/KMJ/1138036904
description: scientific article; zbMATH DE number 3883155