Nowhere minimal CR submanifolds and Levi-flat hypersurfaces
Abstract
A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces.
Cite
@article{arxiv.math/0606141,
title = {Nowhere minimal CR submanifolds and Levi-flat hypersurfaces},
author = {Jiri Lebl},
journal= {arXiv preprint arXiv:math/0606141},
year = {2008}
}
Comments
21 pages; conjecture 2.8 was removed in proof; to appear in J. Geom. Anal