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Regularity of rigid CR hypersurfaces in a sphere

Author: Sung-Yeon Kim
Journal: Proc. Amer. Math. Soc. 139 (2011), 129-137
MSC (2010): Primary 32V30, 32V40; Secondary 53B25, 35N10
Published electronically: September 1, 2010
MathSciNet review: 2729077
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Abstract: Let $ M$ be a germ of a smooth CR manifold of hypersurface type of dimension $ 2n+1$ in a sphere $ S$ of dimension $ 2N+1$ with $ n<N$. In this paper, we show that if $ M$ is rigid and if $ N-n<{n}/{2}$, then there exists a complex manifold $ V$ of (complex) dimension $ n+1$ intersecting $ S$ transversally such that $ M=S\cap V$. As a consequence, we show that $ M$ is real analytic.

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Additional Information

Sung-Yeon Kim
Affiliation: Department of Mathematics Education, Kangwon National University, 123 Hyoja-dong, Chuncheon, Kangwon-do, 200-701, Korea

Received by editor(s): October 12, 2009
Published electronically: September 1, 2010
Additional Notes: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (grant number 2009-0067947)
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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