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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 243
Complex Contact Structures and Spin^C Manifolds. A. Moroianu
In this paper we give an alternative (spinorial) proof of C. LeBrun`s theorem stating that a complex contact manifold admitting a Kaehler-Einstein metric of positive scalar curvature is necessarily the twistor space of a quaternionic Kaehler manifold [7]. This theorem was independently obtained by K.-D. Kirchberg, U. Semmelmann and the author, using special eigenspinors of the Dirac operator, but only in half of the possible dimensions ([4], [8], [10]).
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