Related papers: Analyticite des applications CR

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact…

In this paper we solve the problem of analytic classification of plane curves singularities with two branches by presenting their normal forms. This is accomplished by means of a new analytic invariant that relates vectors in the tangent…

Let M be a real analytic manifold, F a bounded complex of constructible sheaves. We show that the Whitney-de Rham complex associated to F is quasi-isomorphic to F.

We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…

It is constructed a Formal Normal Form for a Special Class of Real-Smooth Submanfolds in $\mathbb{C}^{2N}$.

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities…

An expository description of smooth cubic curves in the real or complex projective plane.

This research article introduces the concept of lightlike submanifolds of an indefinite Kenmotsu statistical manifold. Various results on geometry of contact CR and SCR-lightlike submanifolds have been developed. Some characterization…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…

We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.

We define a CR structure on a distinguished hyperplane in $\mathbb{C}^{n+1}$ and the CR sub-Laplacian on this CR manifold. We also define symmetries of the CR sub-Laplacian in general and for this special case construct all of them using…

In this article, we determine the existing condition of cylinders in smooth minimal geometrically rational surfaces over a perfect field. Furthermore, we show that for any birational map between smooth projective surfaces, one contains a…

We establish for smooth projective real curves the equivalent of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

We prove the following CR version of Artin's approximation theorem for holomorphic mappings between real-algebraic sets in complex space. Let $M\subset \C^N$ be a real-algebraic CR submanifold whose CR orbits are all of the same dimension.…

We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.

Local conditions on boundaries of $C^\infty$ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the…

We introduced a new coordinate-free approach to study the Cauchy-Riemann (CR) maps between the real hyperquadrics in the complex projective space. The central theme is based on a notion of orthogonality on the projective space induced by…

We prove the result stated in the title; it is equivalent to the existence of a regular point of the sub-Riemannian exponential mapping. We also prove that the metric is analytic on an open everywhere dense subset in the case of a complete…

In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…