Regularity of rigid CR hypersurfaces in a sphere
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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.References
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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
- Email: sykim87@kangwon.ac.kr
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 129-137
- MSC (2010): Primary 32V30, 32V40; Secondary 53B25, 35N10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10411-2
- MathSciNet review: 2729077