Conformal Geometry of semi-Riemannian Manifolds

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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.