The scalar curvature and the spectrum of the Laplacian of spin manifolds
type: Item
instance of: scholarly article
title: The scalar curvature and the spectrum of the Laplacian of spin manifolds
zbMATH Open document ID: 0634.58036
DOI: 10.1007/BF01449223
author: Kaoru Ono
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164408
review text: The Dirac operator plays an important role in geometry of spin manifolds. For example, Lichnerowicz deduced the Â-genus vanishing theorem for spin manifolds of positive scalar curvature. In this note we give an upper bound of the greatest lower bound of the spectrum of the Laplacian on universal covering spaces of closed spin manifolds of nonvanishing Â-genus.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J20
zbMATH DE Number: 4032673
zbMATH Keywords: Dirac operator
zbMATH Keywords: spin manifolds
zbMATH Keywords: spectrum of the Laplacian
zbMATH Keywords: Atiyah's \(L^ 2\)-index theorem
MaRDI profile type: Publication
cites work: Q4086472
cites work: The index of elliptic operators. III
cites work: Q3657016
cites work: The fundamental group and the spectrum of the Laplacian
cites work: A computation of the equivariant index of the Dirac operator
cites work: The splitting theorem for manifolds of nonnegative Ricci curvature
cites work: Spin and scalar curvature in the presence of a fundamental group. I
cites work: Q4072462
cites work: An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
cites work: A note on curvature and fundamental group
cites work: The fundamental equations of a submersion
description: scientific article; zbMATH DE number 4032673