A mixed Hodge structure on a CR manifold

TL;DR

This paper proposes a mixed Hodge structure on CR manifolds, exploring the relationship between Kohn-Rossi and De Rham cohomologies, which is not well understood.

Contribution

It introduces a mixed Hodge structure on CR manifolds and investigates the connection between Kohn-Rossi and De Rham cohomologies.

Findings

Establishes a framework for mixed Hodge structures on CR manifolds

Clarifies the relationship between Kohn-Rossi and De Rham cohomologies

Abstract

The purpose of this work is to propose a mixed Hodge structure over a CR manifold. As you know, for a CR manifold, Kohn-Rossi cohomology is naturally introduced. However, the relation between Kohn-Rossi cohomology and De Rham cohomology is not so well understood, even in Tanaka's work. We discuss this point.