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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, [email protected]
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Abstract

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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.

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

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