Complex geometry of real symmetric spaces
by
Simon Gindikin
Rutgers University, USA

Plenary Lecture

One of most brilliant achievements of Geometry of XIX century was the observation that many phenomenas of the real geometry have indeed a complex nature. We will discuss several new observantions in this direction which are connected with a devellopment of harmonic analysis on symmetric spaces. It turns out that each Riemann symmetric space has a canonical complex Stein neighborhood - the crown- in which many analytic invariant objects (spherical functions, solutions of invariant differential equations etc) admit holomorphic extensions. The crowns have curious geometrical properties. Another intersting problem is the understanding of a nature of horospheras for pseudo Riemann symmetric spaces, starting of the pseudo hyperbolic spaces. It is completely clear in the Riemann case, but in the general case the natural class of horospheras is too poor, for example, from point of view of the integral geometry. It turns out that in many cases we need to consider complex horosphears in this purely real geometrical situation.

Date received: May 29, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-75.