Complex geometry of real symmetric spaces
Simon Gindikin
(Rutgers University)
Abstract:
One lesson of Sato's ideology of hyperfunctions is that the
analysis on a real manifold X has deep connections with analysis
of the compliment of the complexification XC\X. A
deliberation of similar phenomenons in geometry gives surprising
constructions almost in the elementary geometry. There are complex
horospheres for the real spheres and the natural dual object for
the sphere is a complex manifold. I will discuss from this point
of view some problems of geometry of pseudo Riemannian symmetric
spaces and their applications to analysis.