Embeddability of Smooth Cauchy-Riemann Manifolds

Author

Roman Dwilewicz, Missouri University of Science and TechnologyFollow

Abstract

The main purpose of this paper is to give a sufficient condition for global embeddability of smooth Cauchy-Riemann manifolds (CR-manifolds) into complex manifolds with boundary. Namely, let M be a smooth CR-manifold of real dimension 2n − 1 and CR-dimension n − 1, where n ⩾ 2, which is locally CR-embeddable into a complex manifold. Assume further that the Levi form of M is non-vanishing at each point. The main result of this paper is that such a CR-manifold is globally CR-embeddable into an n-dimensional complex manifold with boundary. Moreover if the Levi form has at each point of M eigenvalues of opposite signs, then M embeds into a complex manifold without boundary.

Recommended Citation

R. Dwilewicz, "Embeddability of Smooth Cauchy-Riemann Manifolds," Annali di matematica Pura ed Applicata, Springer Verlag, Jan 1985.

The definitive version is available at https://doi.org/10.1007/BF01766848

Department(s)

Mathematics and Statistics

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1985 Springer Verlag, All rights reserved.

Publication Date

01 Jan 1985