seminar: Twistor theory of quaternionic Kahler manifolds; an example of a Penrose transform

speaker: Liana Rodica David (Institute of Mathematics of the Romanian Academy)

abstract: The idea of twistor theory is to translate problems of field equations on a manifold into an algebraic or differential geometric language and to use the powerful methods of geometry in the study of these field equations. The simplest situation in which twistor theory can be applied are conformal self-dual four manifolds. To any conformal four manifold (M, c) one can associate an almost complex manifold, which is, by definition, the space Z of complex structures on M which are compatible with the conformal structure. Geometric properties of M are strongly related to properties of Z. For example, the almost complex structure of Z is integrable (and hence Z is a complex manifold) if and only if M is self-dual. In this talk, I will concentrate on the twistor theory of quaternionic and quaternionic Kahler manifolds, which is a natural generalisation of twistor theory of conformal manifolds. I will begin with the definition and most important properties of quaternionic and quaternionic Kahler manifolds. I will define the twistor space for such manifolds and I will give an explicit example of a Penrose tranforms. This Penrose transform identifies solutions of the Penrose operator on the quaternionic manifold with holomorphic sections of a certain holomorphic line bundle over the twistor space. I will study the properties of this transform.

timetable:
Mon 3 Sep, 11:15 - 12:15, Lizzanello
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