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GR: Gravitation und Relativitätstheorie

GR 10: Inertia, Spinors, and Numerical Relativity

GR 10.2: Invited Talk

Thursday, March 18, 1999, 10:45–11:30, AM1

Geometric investigations of spinor field equations — •Helga Baum — Humboldt-Universiät zu Berlin, Math.-Nat. Fakultät II, Institut für Mathematik, 10099 Berlin

There are two conformally covariant differential operators acting on the spinor fields of a Lorentzian spin manifold, the Dirac operator D and the twistor operator P. In the first part of the lecture we discuss geometric properties of Lorentzian manifolds admitting solutions of the twistor equation Pf=0. Special solutions are parallel spinors and Killing spinors. In the second part we discuss some results and open problems concerning the relation between spectral properties of the Dirac operator D and the geometry of the basic Lorentzian spin manifold.