Dirac operators on hypersurfaces of manifolds with negative scalar curvature
type: Item
instance of: scholarly article
title: Dirac operators on hypersurfaces of manifolds with negative scalar curvature
zbMATH Open document ID: 1032.53040
DOI: 10.1023/A:1022808916165
author: Oussama Hijazi
author: Sebastián Montiel
author: A. Roldán
published in: Annals of Global Analysis and Geometry
publication date: 2003-06-09T00:00:00Z
review text: The authors derive a sharp extrinsic lower bound for the first eigenvalues of the intrinsic Dirac operator of certain hypersurfaces which bound a compact domain in a spin manifold of negative scalar curvature. It is shown that the limiting cases are characterized by the existence of imaginary Killing spinors on the domain, and an Alexandrov type theorem is obtained. Contents include: Riemannian spin manifolds and hypersurfaces, bounding hypersurfaces and a Reilly integral inequality, scalar curvature bounded by a negative constant, an eigenvalue boundary value problem, an extrinsic eigenvalue estimate, ambient manifolds with imaginary Killing spinors, hypersurfaces admitting real Killing spinors, and a bibliography containing thirty-four references.
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83C60
zbMATH DE Number: 1924866
zbMATH Keywords: Dirac operator
zbMATH Keywords: killing spinors
zbMATH Keywords: Alexandrov theorem
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
full work available at URL: a:1022808916165
OpenAlex ID: W2146631527
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description: scientific article; zbMATH DE number 1924866