Kohn-Rossi cohomology and the Bochner technique

TL;DR

This paper establishes a vanishing theorem for Betti numbers on certain CR manifolds using the Bochner technique, advancing understanding of geometric properties under curvature conditions.

Contribution

It introduces a new vanishing theorem for Betti numbers on compact, strictly pseudoconvex pseudohermitian manifolds applying the Bochner method in CR geometry.

Findings

Betti numbers vanish under non-negative curvature operator

Application of Bochner technique to CR manifolds

Advancement in understanding geometric constraints in pseudohermitian geometry

Abstract

We prove a vanishing theorem of Betti numbers on compact, strictly pseudoconvex pseudohermitian manifolds with non-negative curvature operator. The proof is by an application of the Bochner technique to the setting of CR manifolds.