Spin c Manifolds and Complex Contact Structures
In this paper we extend our notion of projectable spinors (, Ch.1) 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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