Related papers: Non-embeddable Real Algebraic Hypersurfaces

In this paper, we provide {\em effective} results on the non-embeddability of real-analytic hypersurfaces into a hyperquadric. We show that, for any $N >n \geq 1$, the defining functions $\varphi(z,\bar z,u)$ of all real-analytic…

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurface called {\em the jet transcendence degree}. Using this…

We survey recent developments on rationality problems for algebraic varieties, with a particular emphasis on cycle-theoretic and combinatorial methods and their applications to hypersurfaces.

We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space $\mathbb R^{n+1}$, $n\geq 2$, defined by polynomials of odd degree. Also we prove that the hyperspheres and the round…

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…

We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are…

Some aspects of the geometry of superembeddings and its application to supersymmetric extended objects are discussed. In particular, the embeddings of (3|16) and (6|16) dimensional superspaces into (11|32) dimensional superspace,…

We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical…

It is a longstanding problem to determine the precise relationship between the geodesic length spectrum of a hyperbolic manifold and its commensurability class. A well known result of Reid, for instance, shows that the geodesic length…

We consider the class of Levi nondegenerate hypersurfaces $M$ in $\bC^{n+1}$ that admit a local (CR transversal) embedding, near a point $p\in M$, into a standard nondegenerate hyperquadric in $\Bbb C^{N+1}$ with codimension $k:=N-n$ small…

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.

In this paper we denote a type of affine homogeneous real hypersurface of $\mathbb{C}^3$ and present a classification of homogeneous surfaces of the type (1/2,0). The result was obtained by reducing the classification problem mentioned…

V. Arnold's problem 1987-14 asks whether there exist smooth hypersurfaces in $R^N$ (other than the conics in odd-dimensional spaces) for which the volume of the segment cut by any hyperplane from the body bounded by such a hypersurface is…

In the paper, we construct, for $\lambda>0$, complete embedded and non-convex $\lambda$-hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that $\lambda$-hypersurfaces share a common conclusion on the planar…

We give a complete description and classification of locally homogeneous real hypersurfaces in $\mathbb C^3$. Various groups of mathematicians have been studying this problem in the last 25 years, and several significant classes of…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…

Perez proved some $L^2$ inequalities for closed convex hypersurfaces immersed in the Euclidean space $\mathbb{R}^{n+1}$, more generally, for closed hypersurfaces with non-negative Ricci curvature, immersed in an Einstein manifold. In this…

We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Q^m for m > 2. We show that m is even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space CP^k…

We study the structure of complex points on real surfaces, embedded into complex Elliptic surfaces. We show, for example, that any compact surface has a totally real embedding into a blow-up of a K3 surface. We also exhibit smooth disc…