The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on April 28, 2022 at 1:00 pm (UTC+3)  in Room 478 of IMI.

A talk on:

Isotropic Killing vector fields and structures on complex surfaces

 will be delivered by Gueo Grantcharov, Florida International University, USA.

Everybody is invited.

Abstract. In a 4-dimensional vector space with scalar product of signature (2,2), two independent vectors spanning a maximal isotropic (null) plane determine a canonical action of the para-quaternioins. We noticed that on an oriented 4-manifold with such pseudo-Riemannian metric, existence of two isotropic (null) Killing vector fields leads to integrability of the induced structure – called para-hypercomplex, and the metric is anti-selfdual. Using the Kodaira classification one can describe the topology of the underlying 4-manifold in the compact case. In this talk, examples of such structures on several of the 4-manifolds will be provided and some restrictions for a compact complex surface to admit split signature Hermitian metric with one non-vanishing null Killing vector field will be established. The talk is based on a joint project with J. Davidov and O. Mushkarov.