Spinc Manifolds and Complex Contact Structures
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- Moroianu, A. Comm Math Phys (1998) 193: 661. doi:10.1007/s002200050343
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In this paper we extend our notion of projectable spinors (, Ch.1) to the framework of Spinc 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.