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Nonexistence of Homogeneous Levi-Flat Hypersurfaces in ${\mathbb{C}\mathbb{P}}^2$

Mathematics
We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP2. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CPn for n>2 is well known, the case n=2 remains open.
Abdel Rahman Al-Abdallah
doaj   +1 more source

REAL HYPERSURFACES IN COMPLEX MANIFOLDS [PDF]

Acta Mathematica, 1974
J. K. Moser, J. K. Moser, Shiing-Shen Chern, Shiing-Shen Chern   +3 more
openaire   +4 more sources

Real hypersurfaces of a complex hyperbolic space

Journal of the Mathematical Society of Japan, 1985
In this paper, using focal point theory, the author classifies real hypersurfaces of a complex hyperbolic space with a few principal curvatures, giving some examples of such type of hypersurfaces. Also, he proves that there exists no Einstein real hypersurfaces in the complex hyperbolic space and he classifies those that satisfy a weaker condition on ...
openaire   +4 more sources

Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric

International Electronic Journal of Geometry, 2018
The article is concerned with the study of real hypersurfaces of the complex quadric Q. We establish B. Y. Chen’s inequalities for real hypersurfaces of the complex quadric Q and by considering the equality case, we obtain some consequences.
P. Bansal, S. Uddin, M. Shahid
semanticscholar   +1 more source

On real forms of Fermat hypersurfaces

, 2023
In this paper, we compute the number of real forms of Fermat hypersurfaces for degree $d \ge 2$ except the degree 4 surface case, and give explicit descriptions of them.
openaire   +2 more sources

Real hypersurfaces of complex projective spaces

Mathematische Annalen, 1983
Let P"(~) denote the complex projective space with Fubini-Study metric of constant holomorphic sectional curvature 4 and suppose m >2. It is well-known that there does not exist a totally umbilical real hypersurface M of P"(C) (see Tashiro and Tachibana [7]).
openaire   +3 more sources

Real hypersurfaces in unimodular complex surfaces

, 2004
A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well.
Bryant, Robert L.
core   +2 more sources

Real hypersurfaces in a complex projective space with constant principal curvatures [PDF]

, 1975
Ryoichi Takagi
openalex   +1 more source

What Is a Simple Liquid?

Physical Review X, 2012
This paper is an attempt to identify the real essence of simplicity of liquids in John Locke’s understanding of the term. Simple liquids are traditionally defined as many-body systems of classical particles interacting via radially symmetric pair ...
Trond S. Ingebrigtsen, Thomas B. Schrøder, Jeppe C. Dyre   +2 more
doaj   +1 more source

Complex submanifolds in real-analytic pseudoconvex hypersurfaces [PDF]

, 1977
Klas Diederich, John Erik Fornæss
openalex   +1 more source