Connected sum of spherical CR manifolds with positive CR Yamabe constant

TL;DR

This paper proves that the connected sum of two closed spherical CR manifolds with positive CR Yamabe constant also admits a spherical CR structure maintaining a positive CR Yamabe constant, extending the class of such manifolds.

Contribution

It demonstrates that the connected sum operation preserves the positive CR Yamabe constant in spherical CR manifolds, a new result in CR geometry.

Findings

Connected sum of two spherical CR manifolds with positive CR Yamabe constant admits a similar structure.

The positive CR Yamabe constant property is preserved under connected sum.

The result extends the understanding of CR structures on complex manifolds.

Abstract

Suppose $M_{1}$ and $M_{2}$ are two closed (compact with no boundary) spherical CR manifolds with positive CR Yamabe constant. In this note, we show that the connected sum of $M_{1}$ and $M_{2}$ also admits a spherical CR structure with positive CR Yamabe constant.