Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-19T01:43:35.335Z Has data issue: false hasContentIssue false
  • English
  • Français

Complete system of finite order for the embeddings of pseudo-hermitian manifolds into ℂN+1

Published online by Cambridge University Press:  22 January 2016

Sung-Yeon Kim
Sung-Yeon Kim*
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, sykim@math.snu.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let (M, ν, θ) be a real analytic (2n+1)-dimensional pseudo-hermitian manifold with nondegenerate Levi form and F be a pseudo-hermitian embedding into ℂn+1. We show under certain generic conditions that F satisfies a complete system of finite order. We use a method of prolongation of the tangential Cauchy-Riemann equations and pseudo-hermitian embedding equation. Thus if F ∈ Ck (M) for sufficiently large k, F is real analytic. As a corollary, if M is a real hypersurface in ℂn+1, then F extends holomorphically to a neighborhood of M provided that F is sufficiently smooth.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 155 , 1999 , pp. 189 - 205
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

[BHR] Baouendi, M. S., Huang, X. and Rothschild, L. P., Nonvanishing of the differential of holomorphic mappings at boundary points, Math. Res. Letter., 2 (1995), 737–750.Google Scholar
[B] Boggess, A., CR manifolds and tangential Cauchy Riemann complex, CRC Press, 1991.Google Scholar
[CM] Chern, S. S. and Moser, J. K., Real hypersurfaces in complex manifolds, Acta Math., 133 (1974), 219–271.Google Scholar
[H] Han, C. K., Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms, Math. Ann., 309 (1997), 401–409.CrossRefGoogle Scholar
[Ha1] Hayashimoto, A., On the complete system of finite order for CR mappings and its application, Osaka J. Math., 35 (1998), 617–628.Google Scholar
[Ha2] Hayashimoto, A., On the relation between the holomorphic extendibility theorems and the finiteness property, to appear in Contemp. Math. Amer. Math. Soc.Google Scholar
[HY] Han, C. K. and Yoo, J. N., A note on E. Cartan’s method of equivalence and local invariants for isometric embeddings of Riemannian manifolds, J. Korean Math. Soc., 34 (1997), no. 4, 771–790.Google Scholar
[M] Moser, J. K., Holomorphic equivalence and normal forms of hypersurfaces, Proc. of Sympos. in Pure Math., 27 (1975), 109–112.Google Scholar
[O] Olver, P. J., Applications of Lie groups to differential equations, Second edition, Springer-Verlag, 1996.Google Scholar
[T] Tomassini, G., Trace delle funzioni olomorfe sulle sottovarieta analitische reali d’una varieta complessa, Ann. Scuola Norm. Sup. Pisa, 20 (1966), 31–43.Google Scholar
[W] Webster, S., Pseudohermitian structure on a real hypersurface, J. Diff. Geom., 13 (1978), 25–41.Google Scholar