EVENT DETAILS AND ABSTRACT

Title: Geometry of twistor spaces
Speaker: Professors J. Davidov and O.Mushkarov
Speaker Info: Bulgarian Academy of Sciences
Brief Description:
Special Note:
Abstract:

The Twistor theory has its origin in Mathematical Physics. Inspired by the Penrose programme, Atiyah, Hitchin and Singer developed this theory on 4-dimensional Riemannian manifolds. The twsitor space of such a manifold $M$ is the bundle $J(M)\to M$ of all complex structures on the tangent spaces of $M$ compatible with the metric. The 6-manifold $J(M)$ admits two natural almost complex structures, traditionally denoted by $J_1$ and $J_2$, introduced, respectively, by Atiyah, Hitchin, Singer and Eells, Salamon. This construction works also in higher dimensions and the almost complex structures $J_1$ and $J_2$ have been studied in different aspects. In this talk we shall give a survey of some recent results on the geometry of twistor spaces in the following directions: - Penrose transform and Ward correspondance. Applications. - Harmonic maps into Riemannian manifolds and holomorphic curves in twistor spaces. - Hermitian geometry of twistor spaces.