Kohn-Rossi cohomology and the Bochner technique

2025/05/30 by Tao, Alex
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.24184

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.

Citations

• Curvature of the Second kind and a conjecture of Nishikawa
• Frankel Conjecture and Sasaki geometry
• Manifolds with positive curvature operators are space forms

Related

• Integral Curvature Bounds and Betti Numbers
• Topology of Kähler manifolds with weakly pseudoconvex boundary
• On the CR analogue of Frankel conjecture and a smooth representative of the first Kohn-Rossi cohomology group
• A Bochner Technique For Foliations With Non-Negative Transverse Ricci Curvature
• Solution of the tangential Kohn Laplacian on a class of non-compact CR\n manifolds