Mostow's Fibration for canonical embeddings of compact homogeneous CR manifolds

TL;DR

This paper introduces a class of compact homogeneous CR manifolds with Mostow fibrations, linking their CR cohomology to Dolbeault cohomology of their complex realizations, enhancing understanding of their geometric structures.

Contribution

It defines a new class of CR manifolds with specific fibrations and establishes isomorphisms between their CR and Dolbeault cohomology groups.

Findings

Established isomorphisms between CR and Dolbeault cohomology groups.

Defined a class of CR manifolds with canonical complex realizations.

Linked geometric fibrations to cohomological properties.

Abstract

We define a class of compact homogeneous CR manifolds which are bases of Mostow fibrations having total spaces equal to their canonical complex realizations and Hermitian fibers. This is used to establish isomorphisms between their tangential Cauchy-Riemann cohomology groups and the corresponding Dolbeault cohomology groups of the embeddings.