Spin^c Manifolds and Complex Contact Structures

Andrei Moroianu (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu. Spin^c Manifolds and Complex Contact Structures. Communications in Mathematical Physics, 1998, 193, pp.661-673. ⟨10.1007/s002200050343⟩. ⟨hal-00125990⟩