A comparison theorem for eigenvalues of the covariant Laplacian
type: Item
instance of: scholarly article
title: A comparison theorem for eigenvalues of the covariant Laplacian
zbMATH Open document ID: 0716.58030
DOI: 10.1016/0022-1236(90)90017-F
author: Shojiro Manabe
author: Ichiro Shigekawa
published in: Journal of Functional Analysis
publication date: 1990-01-01T00:00:00Z
review text: The minimax principle is employed to bound the eigenvalues \(\lambda_ n\), of a covariant Laplacian associated to a connection on a vector bundle, above by the eigenvalues \(\mu_ n\), of a corresponding scalar Laplacian. If there exists a non-vanishing eigensection, of the bundle, and \(n=0\), then equality is attained. Some examples are given.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4180380
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: minimax principle
zbMATH Keywords: eigenvalues
zbMATH Keywords: covariant Laplacian
zbMATH Keywords: connection
zbMATH Keywords: vector bundle
reviewed by: Harold Donnelly
MaRDI profile type: Publication
cites work: Q3756011
cites work: Q3753202
cites work: Q5731354
cites work: Q3694367
cites work: Q3749431
cites work: Q3719576
cites work: Q3709561
cites work: Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold
cites work: Lectures on stochastic differential equations and Malliavin calculus
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description: scientific article; zbMATH DE number 4180380