Some estimates of total tension and their applications
type: Item
instance of: scholarly article
title: Some estimates of total tension and their applications
zbMATH Open document ID: 0614.53042
published in: Kodai Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The main result of this paper is an estimate of the total tension \(\int | \Delta f|^ 2\) for maps \(f: M^ n\to {\mathbb{R}}^ n\) in terms of the eigenvalues \(\lambda_ 1\) and \(\lambda_ 2\) of \((M^ n,g)\). As an application sharp inequalities involving only \(\lambda_ 1\) and \(\lambda_ 2\) are obtained for compact minimal submanifolds of rank-one symmetric spaces.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 3994470
zbMATH Keywords: eigenvalues of the Laplace operator
zbMATH Keywords: total tension
zbMATH Keywords: minimal submanifolds
author: Bang-Yen Chen
reviewed by: Ulrich Pinkall
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037364
OpenAlex ID: W1989921153
cites work: Spherical submanifolds which are of 2-type via the second standard immersion of the sphere
cites work: Q3884788
cites work: Q3219597
cites work: Q3322795
cites work: Q3702922
cites work: Energy, tension and finite type maps
cites work: A Report on Harmonic Maps
cites work: Curvature pinching and eigenvalue rigidity for minimal submanifolds
cites work: On locally symmetric Kaehler submanifolds in a complex projective space
cites work: On spectral geometry of Kähler submanifolds
cites work: Eigenvalue inequalities for minimal submanifols and P-manifolds
cites work: Planar geodesic immersions
cites work: Spectral geometry of Kaehler submanifolds of a complex projective space
DOI: 10.2996/KMJ/1138037364
description: scientific article; zbMATH DE number 3994470