Orbits of real forms in complex flag manifolds

TL;DR

This paper studies the geometric and topological properties of real form orbits in complex flag manifolds, focusing on conditions like finite type, Levi non-degeneracy, and fibrations, to understand their structure.

Contribution

It provides a detailed analysis of the CR geometry, fibrations, and topological features of real form orbits in complex flag manifolds, highlighting new conditions and properties.

Findings

Characterization of finite type and Levi non-degeneracy conditions

Analysis of canonical G_0-equivariant fibrations

Topological properties of the orbits

Abstract

We investigate the $CR$ geometry of the orbits $M$ of a real form $G_0$ of a complex simple group $G$ in a complex flag manifold $X=G/Q$. We are mainly concerned with finite type, Levi non-degeneracy conditions, canonical $G_0$-equivariant and Mostow fibrations, and topological properties of the orbits.