The Szeg\"o kernel on a class of noncompact CR manifolds of high codimension

TL;DR

This paper generalizes Nagel's formula to compute the Szeg"o kernel on certain noncompact CR manifolds with high codimension, analyzing its relation to the control metric.

Contribution

It extends the explicit computation of the Szeg"o kernel to a broader class of noncompact CR manifolds with complex and real tangent directions.

Findings

Derived a generalized formula for the Szeg"o kernel

Connected the size of the Szeg"o kernel to the control metric

Provided insights into the geometry of high codimension CR manifolds

Abstract

We generalize Nagel's formula for the Szeg\"o kernel and use it to compute the Szeg\"o kernel on a class of noncompact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szeg\"o kernel.