A BLW inequality for vector bundles and applications to spectral bounds
type: Item
instance of: scholarly article
title: A BLW inequality for vector bundles and applications to spectral bounds
zbMATH Open document ID: 0696.58046
DOI: 10.1016/0022-1236(89)90058-X
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: The authors prove a non-commutative Bochner-Lichnerowicz-Weitzenböck formula for the Bochner Laplacian \(B\) acting on sections of a real finite dimensional \(C^*\)-algebra bundle. Then they deduce a lower bound for the spectrum \(\sigma(-B)\) of \(-B\) acting on a Euclidean vector bundle which has no non-vanishing sections. If \(E_{\mathrm{sc}}\) denotes the smallest non-zero eigenvalue of the scalar Laplacian then for \(E\in \sigma(-B)\) either \(E>1/d^2\) or \(E\geq c\cdot E_{\mathrm{sc}}\) where \(d=\mathrm{diam } M\) and \(c\) is an explicit constant depending on the Ricci curvature of the manifold \(M\) and on the curvature and the current of the bundle.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 4140892
zbMATH Keywords: Bochner-Lichnerowicz-Weitzenböck formula for the Bochner Laplacian
zbMATH Keywords: spectral bounds
author: E. Brian Davies
author: Oscar S. Rothaus
MaRDI profile type: Publication
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Wikidata QID: Q125925036
description: scientific article; zbMATH DE number 4140892