Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On CR embeddings of strictly pseudoconvex hypersurfaces into spheres in low dimensions


Authors: Peter Ebenfelt and André Minor
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 32H02, 32V30
Published electronically: May 21, 2014
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It follows from the 2004 work of the first author, X.Huang, and D. Zaitsev that any local CR embedding $ f$ of a strictly pseudoconvex hypersurface $ M^{2n+1}\subset \mathbb{C}^{n+1}$ into the sphere $ \mathbb{S}^{2N+1}\subset \mathbb{C}^{N+1}$ is rigid, i.e. any other such local embedding is obtained from $ f$ by composition with an automorphism of the target sphere $ \mathbb{S}^{2N+1}$, provided that the codimension $ N-n<n/2$. In this paper, we consider the limit case $ N-n=n/2$ in the simplest situation where $ n=2$, i.e. we consider local CR embeddings $ f\colon M^5\to \mathbb{S}^7$. We show that there are at most two different local embeddings up to composition with an automorphism of $ \mathbb{S}^7$. We also identify a subclass of 5-dimensional, strictly pseudoconvex hypersurfaces $ M^5$ in terms of their CR curvatures such that rigidity holds for local CR embeddings $ f\colon M^5\to \mathbb{S}^7$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 32H02, 32V30

Retrieve articles in all journals with MSC (2010): 32H02, 32V30


Additional Information

Peter Ebenfelt
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
Email: pebenfel@math.ucsd.edu

André Minor
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
Email: aminor@math.ucsd.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06085-6
PII: S 0002-9947(2014)06085-6
Received by editor(s): August 17, 2012
Published electronically: May 21, 2014
Additional Notes: The authors were supported in part by DMS-1001322.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.