Introduction

Abstract

The four main subjects in the geometry of complex homogeneous-bounded domains are: (i) the classification, (ii) the realization as Siegel domains, (iii) determination of full holomorphic automorphism groups and (iv) the analytic or geometric relationship between the Šilov boundaries and the domains themselves. During the 1960’s-1970s these subjects had been the main goals for research in this field. On the other hand, the following natural question arises: What kind of homogeneous domains are there in the complement of a given symmetric domain in ${\mathbb{C}^n}$? This question leads us to study semisimple pseudo-Hermitian symmetric spaces. The infinitesimal classification of such symmetric spaces is included in Berger’s work [1].