The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 6, 2018 at 14:00 in Room 478 of IMI.
A talk on:

Generalized Geometry in the Sense of Hitchin and Generalized Twistor Spaces

will be delivered by Johann Davidov, IMI-BAS.

Everybody is invited.

Abstract. The concept of generalized complex geometry has been introduced by Nigel Hitchin and developed further by his students M. Gualtieri, G. Ca-valcanti, F. Witt as well as by many other mathematicians and physicists (including Hitchin himself). It generalizes both the concept of a complex structure and that of a symplectic one and can be considered as a complex analog of the notion of a Dirac structure introduced by T. Courant and A. Weinstein to unify Poisson and symplectic geometries. In this talk basic facts about the generalized geometry will be presented. Then the twistor construction for Riemannian manifolds will be extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the manifold compatible with the given generalized metric. This space admits natural generalized almost complex structures whose integrability conditions will be discussed. An interesting feature of the generalized twistor spaces, which usual twistor spaces do not admit, is the existence of intrinsic isomorphisms.

The talk is based on the author’s paper “Generalized metrics and generalized twistor spaces” which will soon appear in Mathematische Zeitschrift.