Kohn-Rossi cohomology of spherical CR manifolds
Yuya Takeuchi
TL;DR
This paper establishes vanishing theorems for Kohn-Rossi cohomology on spherical CR manifolds using a canonical contact form and Weitzenböck formulas, demonstrating optimal results in certain cases.
Contribution
It introduces new vanishing theorems for Kohn-Rossi cohomology on spherical CR manifolds utilizing a canonical contact form derived from Patterson-Sullivan measure.
Findings
Vanishing theorems for Kohn-Rossi cohomology established.
Use of Patterson-Sullivan measure to define canonical contact form.
Results shown to be optimal in some cases.
Abstract
We prove some vanishing theorems for the Kohn-Rossi cohomology of some spherical CR manifolds. To this end, we use a canonical contact form defined via the Patterson-Sullivan measure and Weitzenb\"{o}ck-type formulae for the Kohn Laplacian. We also see that our results are optimal in some cases.
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Taxonomy
TopicsGeometry and complex manifolds · Holomorphic and Operator Theory · Advanced Algebra and Geometry