Related papers: Real Hypersurfaces of Non-Flat Complex Space Forms…
We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian…
In this paper, we investigate the spectral properties of the Jacobi operator for immersed surfaces with nonpositive Euler characteristic, extending previous results in the field. We first prove a sharp upper bound for the second eigenvalue…
We consider hypersurfaces of finite type in a direct product space ${\mathbb R}^2 \times {\mathbb R}^2$, which are analogues to real hypersurfaces of finite type in ${\mathbb C}^2$. We shall consider separately the cases where such…
The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential $1$-forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are…
In this paper we analyze the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing…
We call a real algebraic hypersurface in $(\mathbb{C}^*)^n$ simplicial if it is given by a real Laurent polynomial in $n$-variables that has exactly $n+1$ monomials with non-zero coefficients and such that the convex hull in $\mathbb{R}^n$…
We study the relation between a certain graded part of the Jacobian ring of a projective hypersurface and a certain graded quotient for the Hodge filtration of its primitive cohomology, in the case that the hypersurface has at most isolated…
We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are…
We study real Campedelli surfaces up to real deformations and exhibit a number of such surfaces which are equivariantly diffeomorphic but not real deformation equivalent.
Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ are given in terms of the graded Betti numbers of the minimal free resolution of the corresponding Jacobian algebra.…
In this paper, we study locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of affine metric. As the main result, we classify such…
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,…
This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic…
The main two families of real hypersurfaces in complex space forms are Hopf and ruled. However, very little is known about real hypersurfaces in the indefinite complex projective space $\cpn$. In a previous work, Kimura and the second…
Let X be a hypersurface of a Mori dream space Z. We provide necessary and sufficient conditions for the Cox ring R(X) of X to be isomorphic to R(Z)/(f), where R(Z) is the Cox ring of Z and f is a defining section for X. We apply our results…
We investigate the structure of real hypersurfaces with isometric Reeb flow in Kaehler manifolds. As an application we classify real hypersurfaces with isometric Reeb flow in irreducible Hermitian symmetric spaces of compact type.
We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat…
We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces…
The object of this paper is to introduce new classes of hypersurfaces of almost product-like statistical manifolds. The main properties and relations on $K-$para contact, para cosymplectic, para Sasakian and conformal hypersurfaces are…
Given a real algebraic variety $X$ of dimension $n$, a very ample divisor $D$ on $X$ and a smooth closed hypersurface $\Sigma$ of $\mathbf{R}^n$, we construct real algebraic hypersurfaces in the linear system $|mD|$ whose real locus…