Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension >= 3
Complex Variables
2016-09-07 v1 Differential Geometry
Abstract
In this paper we prove the following theorem. Main Theorem. Let n >= 3 and m >= 3n/2 +7. Then there exists no C^m Levi-flat real hypersurface M in P_n. The condition that M is Levi-flat means that when M is locally defined by the vanishing of a C^m real-valued function f, at every point of M the restriction of d d-bar f to the complex tangent space of M is identically zero. The case of the nonexistence of C^\infty Levi-flat real hypersurface in P_2 is motivated by problems in dynamical systems in P_2.
Keywords
Cite
@article{arxiv.math/0005307,
title = {Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension >= 3},
author = {Yum-Tong Siu},
journal= {arXiv preprint arXiv:math/0005307},
year = {2016}
}
Comments
27 pages, published version, abstract added in migration