Orbits of real forms, Matsuki duality and CR-cohomology

TL;DR

This paper explores the connection between tangential CR cohomology on certain compact homogeneous CR manifolds and the Dolbeault cohomology of their complex embeddings, highlighting dualities and relationships.

Contribution

It establishes a link between CR cohomology groups and Dolbeault cohomology in the context of homogeneous CR manifolds, advancing understanding of their geometric and algebraic structures.

Findings

Identifies relationships between CR and Dolbeault cohomology groups.

Provides insights into the structure of compact homogeneous CR manifolds.

Highlights the role of Matsuki duality in cohomological contexts.

Abstract

We discuss the relationship between some groups of tangential CR cohomology of some compact homogeneous CR manifolds and the corresponding Dolbeault cohomology groups of their canonical complex embeddings.