The Dirac operator on Lorentzian spin manifolds and the Huygens property
type: Item
instance of: scholarly article
title: The Dirac operator on Lorentzian spin manifolds and the Huygens property
zbMATH Open document ID: 0913.34074
DOI: 10.1016/S0393-0440(96)00045-9
author: Helga Baum
published in: Journal of Geometry and Physics
publication date: 1999-01-06T00:00:00Z
review text: The author investigates the Huygens property for the square \(D^2\) of the Dirac operator of a Lorentzian spin manifold of even dimension \(n\geq 4\). She proves that the operator \(D^2-K\) is of Huygens type if the underlying Lorentzian spin manifold has constant sectional curvature \(K\). Furthermore, \(D^2\) is of Huygens type on a plane wave manifold. Finally, the square of twisted Dirac operators on four-dimensional manifolds is considered. The author proves that the Huygens property of these operators implies that the coupling connection is flat and that the manifold belongs to one of three special classes of Lorentzian manifolds.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 81R25
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 57R15
zbMATH DE Number: 1051641
zbMATH Keywords: Dirac operator
zbMATH Keywords: Lorentzian spin manifolds
zbMATH Keywords: Huygens principle
reviewed by: Katharina Habermann
MaRDI profile type: Publication
cites work: Q3668451
cites work: Normally hyperbolic operators, the Huygens property and conformal geometry
cites work: Huygens' principle and integrability
cites work: Q3767982
cites work: Q4076197
cites work: Ein Beispiel einer nichttrivialen Huygensschen Differentialgleichung mit vier unabhängigen Variablen
cites work: Q4040088
cites work: Huygens' principle and Hadamard's conjecture
cites work: Fundamental solutions of invariant differential operators on symmetric spaces
cites work: On Huygens' Principle for the Relativistic Higher Spin Wave Equations of Buchdahl and Wünsch in Presence of a Gravitational and an Electromagnetic Field
cites work: Q3995493
cites work: Zur Gültigkeit des Huygensschen Prinzips bei einer speziellen Metrik
cites work: RIEMANNsche Räume mit ebenfrontiger und mit ebener Symmetrie
cites work: Helmholtz operators on harmonic manifolds
cites work: Q3894693
cites work: Q3920065
cites work: Selbstadjungierte huygenssche Differentialgleichungen zweiter Ordnung für nichtskalare Spintensorfelder
cites work: Q4305466
description: scientific article; zbMATH DE number 1051641