On Three-Dimensional CR Yamabe Solitons

In this paper, we investigate the geometry and classification of three-dimensional CR Yamabe solitons and pseudo-gradient CR Yamabe solitons. In the compact case, we obtain a classification result of three-dimensional CR Yamabe solitons under the assumption that their potential functions are in the...

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Bibliographic Details
Published in:The Journal of geometric analysis 2018, Vol.28 (1), p.335-359
Main Authors: Cao, Huai-Dong, Chang, Shu-Cheng, Chen, Chih-Wei
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Classification
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Solitary waves
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Summary:In this paper, we investigate the geometry and classification of three-dimensional CR Yamabe solitons and pseudo-gradient CR Yamabe solitons. In the compact case, we obtain a classification result of three-dimensional CR Yamabe solitons under the assumption that their potential functions are in the kernel of the CR Paneitz operator. In addition, we obtain a structure theorem on the diffeomorphism types of complete three-dimensional pseudo-gradient CR Yamabe solitons (shrinking, steady, or expanding) of vanishing torsion.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-017-9822-3