Conformal Geometry of semi-Riemannian Manifolds

• Applicant: Professor Dr. Hans-Bert Rademacher
• Subject Area: Mathematics
• Term: from 2005 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 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 Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry
• Participating Person: Professor Dr. Wolfgang Kühnel