The Dirac operator on space forms of positive curvature
type: Item
instance of: scholarly article
title: The Dirac operator on space forms of positive curvature
zbMATH Open document ID: 0848.58046
published in: Journal of the Mathematical Society of Japan
publication date: 1996-11-04T00:00:00Z
review text: The Dirac operator is an elliptic differential operator naturally associated to a Riemannian spin manifold. There are only few manifolds for which one can explicitly compute the Dirac spectrum. In the present paper Killing spinors are used to determine the Dirac eigenvalues of spheres with constant curvature. They take the simple form \(\lambda = \pm ({1\over 2} \cdot\) dimension \(+ k)\), \(k \in \mathbb{N}_0\). Then the Dirac spectrum of quotients of the sphere (e.g. real hyperbolic spaces) is encoded into a Poincaré series. This is used to characterize space forms with many Killing spinors generalizing a result by A. Franc and to construct Dirac isospectral non-isometric space forms. They have metacyclic fundamental groups.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 894114
zbMATH Keywords: spherical space forms
zbMATH Keywords: isospectral manifolds
zbMATH Keywords: Dirac operator
zbMATH Keywords: Killing spinors
author: Christian Bär
reviewed by: Christian Bär
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04810069
OpenAlex ID: W1982134436
DOI: 10.2969/JMSJ/04810069
description: scientific article; zbMATH DE number 894114