Spin^c Manifolds and Complex Contact Structures

Abstract : In this paper we extend our notion of projectable spinors to the framework of Spin^c manifolds and deduce the basic formulas relating spinors on the base and the total space of Riemannian submersions with totally geodesic one-dimensional fibres. Some geometric applications concerning positive Kähler-Einstein complex contact manifolds (e.g. their characterisation as twistor spaces over positive quaternionic Kähler manifolds) are also given.
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Andrei Moroianu. Spin^c Manifolds and Complex Contact Structures. Communications in Mathematical Physics, Springer Verlag, 1998, 193, pp.661-673. 〈10.1007/s002200050343〉. 〈hal-00125990〉

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