Szegő kernel expansion and equivariant embedding of CR manifolds with circle action

Abstract

Let $X$ be a compact strongly pseudoconvex CR manifold with a transversal CR $S^1$-action. In this paper, we establish the asymptotic expansion of Szegő kernels of positive Fourier components and by using the asymptotics, we show that $X$ can be equivariant CR embedded into some ${\mathbb{C}}^N$ equipped with a simple $S^1$-action. An equivariant embedding of quasi-regular Sasakian manifold is also derived.

final version, title changed

References in corpus (2)

• Szegö kernel asymptotics and Morse inequalities on CR manifolds with $S^1$ action
• Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with $S^1$-action

Cited by in corpus (2)

• On the stability of equivariant embedding of compact CR manifolds with circle action
• On a Holomorphic Family of Stein Manifolds with Strongly Pseudoconvex Boundaries