Conformal Geometry of semi-Riemannian Manifolds

• Antragsteller: Professor Dr. Hans-Bert Rademacher
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2005 bis 2010
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 5453380

Conformal Symmetries have been studied in General Relativity during many decades, and many concepts in differential geometry and mathematical physics are conformally invariant. In dimension four vacuum spacetimes with non-trivial conformal symmetries are pp-metrics first introduced by Brinkmann. We plan to introduce an extension of pp-metrics (which we call generalized Brinkmann spaces) and study the following questions in the two parts of our project:1. Conformal Symmetries of Generalized Brinkmann Spaces For an appropriate generalization of pp-metrics including pure radiation metrics with a lightlike Killing field we study conformal symmetries and conformal transformations inside the class of these metrics.2. Spin-Geometry of Generalized Brinkmann Spaces We plan to study conformal compactifications of pp-metrics resp. generalized Brinkmann spaces admitting twistor spinors with zeros. Another line of investigation will be concerned with solutions of generalized Killing spinor equations and the construction of supersymmetries.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1154: Globale Differentialgeometrie
• Beteiligte Person: Professor Dr. Wolfgang Kühnel