On Three-dimensional CR Yamabe Solitons

TL;DR

This paper studies three-dimensional CR Yamabe solitons, providing classification results for compact cases with constant scalar curvature and structure theorems for complete solitons with vanishing torsion.

Contribution

It offers new classification results for 3D CR Yamabe solitons, especially under specific curvature and potential function conditions.

Findings

Compact CR Yamabe solitons have constant Tanaka-Webster scalar curvature.

Classification achieved for solitons with potential functions in the kernel of the CR Paneitz operator.

Structure theorem established for complete 3D pseudo-gradient CR Yamabe solitons with vanishing torsion.

Abstract

In this paper, we investigate the geometry and classification of three-dimensional CR Yamabe solitons. In the compact case, we show that any 3-dimensional CR Yamabe soliton must have constant Tanaka-Webster scalar curvature; we also obtain a classification under the assumption that their potential functions are in the kernel of the CR Paneitz operator. In the complete case, we obtain a structure theorem on the diffeomorphism types of complete 3-dimensional pseudo-gradient CR Yamabe solitons (shrinking, or steady, or expanding) of vanishing torsion.