Mathematics
Document Type
Article
Abstract
We consider the sphere (Formula presented.) equipped with its standard contact form. In this paper, we construct explicit contact forms on (Formula presented.), which are conformal to the standard one and whose related Webster metrics have constant Webster curvature; in particular, it is positive if (Formula presented.). As main applications, we provide two perturbative results. In the first one, we prove the existence of infinitely many contact forms on (Formula presented.) conformal to the standard one and having constant Webster curvature, where (Formula presented.) is a small perturbation of (Formula presented.). In the second application, we show that there exist infinitely many bifurcating branches of periodic solutions to the CR Yamabe problem on (Formula presented.) having constant Webster curvature. © 2023 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH.
Publication Title
Mathematische Nachrichten
Publication Date
3-2024
Volume
297
Issue
3
First Page
943
Last Page
961
ISSN
0025-584X
DOI
10.1002/mana.202200289
Keywords
conformal geometry, singular contact structures, singular Yamabe problem
Repository Citation
Guidi, Chiara; Maalaoui, Ali; and Martino, Vittorio, "Singular CR structures of constant Webster curvature and applications" (2024). Mathematics. 11.
https://commons.clarku.edu/mathematics/11
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License