Some remarks on the Dirac-Witten operator on pseudo-Riemannian manifolds
type: Item
instance of: scholarly article
title: Some remarks on the Dirac-Witten operator on pseudo-Riemannian manifolds
zbMATH Open document ID: 1250.53067
author: Xu Xu
author: Yongfa Chen
published in: Journal of Geometry and Physics
publication date: 2012-08-20T00:00:00Z
reviewed by: Joseph D. Zund
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 6069289
zbMATH Keywords: Dirac-Witten operator
zbMATH Keywords: optimal lower bounds
zbMATH Keywords: intrinsic and extrinsic curvatures
zbMATH Keywords: space-like submanifold
MaRDI profile type: Publication
full work available at URL: j.geomphys.2012.04.009
OpenAlex ID: W1970346561
Wikidata QID: Q115353211
cites work: Q3995493
cites work: Real Killing spinors and holonomy
cites work: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
cites work: Lower eigenvalue estimates for Dirac operators
cites work: A new proof of the positive energy theorem.
cites work: Lower bounds for eigenvalues of the Dirac-Witten operator
cites work: The Dirac-Witten operator on pseudo-Riemannian manifolds
cites work: ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR
cites work: Lower bounds for the eigenvalues of the Dirac operator. II: The submanifold Dirac operator
cites work: The Dirac-Witten operator on spacelike hypersurfaces
cites work: Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary
cites work: A new quasi-local mass and positivity
cites work: The Einstein-Dirac equation on Riemannian spin manifolds
cites work: Lower bounds for the eigenvalues of the Dirac operator
DOI: 10.1016/J.GEOMPHYS.2012.04.009
review text: The authors derive optimal lower bounds on the Dirac-Witten operator on pseudo-Riemannian manifolds. These expressions are exhibited in terms of the intrinsic and extrinsic curvatures, and in a limiting case it is shown that the space-like submanifold is an Einstein manifold if the normal bundle is flat.NEWLINENEWLINE Contents include: An Introduction (which summarizes previous work); Lower bounds for the eigenvalues (which introduces their notation and preliminaries); Conformal lower bounds; Generalized conformal lower bounds; Conformal submanifolds with non-empty boundary; References (with fifteen items).
description: scientific article; zbMATH DE number 6069289