Резюме: 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

Download the abstract (in English)

Резюме: In this talk we will establish the explicit formulas of squeezing functions on doubly connected planar domains in an elementary way. With the same method we will also provide bounds to squeezing functions of higher connected domains. Finally, we will conclude by mentioning other results and further questions about explicit formulas of squeezing functions on planar domains.

Download the abstract (in English)