# Deformations and embeddings of three-dimensional strictly pseudoconvex CR manifolds

@article{Curry2020DeformationsAE, title={Deformations and embeddings of three-dimensional strictly pseudoconvex CR manifolds}, author={Sean N. Curry and Peter Ebenfelt}, journal={arXiv: Complex Variables}, year={2020} }

Abstract deformations of the CR structure of a compact strictly pseudoconvex hypersurface $M$ in $\mathbb{C}^2$ are encoded by complex functions on $M$. In sharp contrast with the higher dimensional case, the natural integrability condition for $3$-dimensional CR structures is vacuous, and generic deformations of a compact strictly pseudoconvex hypersurface $M\subseteq \mathbb{C}^2$ are not embeddable even in $\mathbb{C}^N$ for any $N$. A fundamental (and difficult) problem is to characterize…

## One Citation

Obstruction flat rigidity of the CR 3-sphere

- MathematicsJournal für die reine und angewandte Mathematik
- 2021

Abstract We consider the obstruction flatness problem for small deformations of the standard CR 3-sphere. That rigidity holds for the CR sphere was previously known (in all dimensions) for the case…

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