Related papers: Stark hypersurfaces in complex projective space
In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
Since the work of Ellingsrud and Peskine at the end of 1980s, it has been known that, with the exception of a finite number of families, smooth compact complex surfaces in $\mathbb{P}^4$ with prescribed Chern classes must lie on…
Let $F$ be a homogeneous polynomial in $S = \mathbb{C}[x_0,...,x_n]$. Our goal is to understand a particular polynomial decomposition of $F$; geometrically, we wish to determine when the hypersurface defined by $F$ in $\mathbb{P}^n$…
In this paper, we establish some rigidity theorems for space-like hypersurfaces in Minkowski space by using a Weinberger-type approach with P-functions and integral identities. Firstly, for space-like hypersurfaces $M$ represented as graphs…
It is proved that the geometry of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 is directly connected with the geometry of hypersurfaces of the conformal space C^n. This connection is applied for a construction of an invariant…
A very general hypersurface of dimension $n$ and degree $d$ in complex projective space is rational if $d \leq 2$, but is expected to be irrational for all $n, d \geq 3$. Hypersurfaces in weighted projective space with degree small relative…
We study the holomorphic extendability of smooth CR maps between real analytic strictly pseudoconvex hypersurfaces in complex affine spaces of different dimensions.
Suppose that $f$ defines a singular, complex affine hypersurface. If the critical locus of $f$ is one-dimensional, we obtain new general bounds on the ranks of the homology groups of the Milnor fiber of $f$. This result has an interesting…
This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the…
In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…
The class of surfaces in 3-space possessing nontrivial deformations which preserve principal directions and principal curvatures (or, equivalently, the shape operator) was investigated by Finikov and Gambier as far back as in 1933. We…
Let $x$ be an $m$-dimensional umbilic-free hypersurface in an $(m+1)$-dimensional unit sphere $\mathbb{S}^{m+1}(m\geq3)$. One of important questions is to classify hypersurfaces with two distinct principal curvatures. In this paper, we…
The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since our approach comes from harmonic analysis, we establish…
It is known that the lens space $L(2n,1)$ supports a virtually overtwisted contact structure arising as the boundary of the Milnor fiber of a complex hypersurface singularity. In this article we study the problem of realizing other…
Under a hypothesis on $k$, $d$ and $n$ that is almost the best possible, we prove that for every smooth degree $d$ hypersurface in $P^n$, the $k$-plane sections dominate the moduli space of degree $d$ hypersurface in $P^k$. Using this we…
We show that if the Segre varieties of a strictly pseudoconvex hypersurface in $\mathbb{C}^2$ are extremal discs for the Kobayashi metric, then that hypersurface has to be locally spherical. In particular, this gives yet another…
We characterise the profile curves of non-CMC biconservative rotational hypersurfaces of space forms $N^n(\rho)$ as $p$-elastic curves, for a suitable rational number $p\in[1/4,1)$ which depends on the dimension $n$ of the ambient space.…
The Eckardt hypersurface in $\mathbb{P}^{19}$ parameterizes smooth cubic surfaces with an Eckardt point, which is a point common to three of the $27$ lines on a smooth cubic surface. We describe the cubic surfaces lying on the singular…