Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 477

The Einstein-Dirac equation on Sasakian 3-manifolds

F. Belgun

We prove that a Sasakian 3-manifold admitting a non-trivial solution to the Einstein-Dirac equation has necessarily constant scalar curvature. In the case when this scalar curvature is non-zero, their classification follows then from a result by Th. Friedrich and E.C. Kim. We also prove that a scalar-flat Sasakian 3-manifold admits no local Einstein spinors.

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