相关论文: Classification of simply-transitive Levi non-degen…
We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in $\mathbb{C}^3$ with symmetry algebra of dimension $\geq 6$.
We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By recent results of Kolar, Meylan and Zaitsev, the Lie algebra of infinitesimal CR automorphisms may contain a graded component consisting of nonlinear…
Locally homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^2$ were classified by E.\,Cartan in 1932. In this work, we complete the classification of locally homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$.
We explicitly determine the structure equations of 5-dimensional Levi 2-nondegenerate CR hypersurfaces, using our recently constructed canonical Cartan connection for this class of CR manifolds. We also give an outline of the basic…
We study CR hypersurfaces in $\mathbb{C}^4$ that are Levi degenerate with constant rank Levi form, and moreover finitely nondegenerate. Each of these can be described as a deformation of a model CR hypersurface by adding terms of higher…
We continue our study, initiated in an earlier article, of a class of rigid hypersurfaces in ${\mathbb C}^3$ that are 2-nondegenerate and uniformly Levi degenerate of rank 1, having zero CR-curvature. We drop the restrictive assumptions of…
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…
In this paper, we consider real hypersurfaces $M$ in $\Bbb C^3$ (or more generally, 5-dimensional CR manifolds of hypersurface type) at uniformly Levi degenerate points, i.e. Levi degenerate points such that the rank of the Levi form is…
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 consider the problem of describing the local biholomorphic equivalence class of a real-analytic hypersurface $M$ at a distinguished point $p_0\in M$ by giving a normal form for such objects. In order for the normal form to carry useful…
We solve the Levi-flat Plateau problem in the following case. Let $M \subset {\mathbb C}^{n+1}$, $n \geq 2$, be a connected compact real-analytic codimension-two submanifold with only nondegenerate CR singularities. Suppose $M$ is a…
We develope in great computational details the classical Cartan equivalence problem for Levi-nondegenerate C^6-smooth real hypersurfaces M^3 in C^2, performing all calculations effectively in terms of a (local) graphing function \varphi. In…
Fels-Kaup (Acta Mathematica 2008) classified homogeneous $\mathfrak{C}_{2,1}$ hypersurfaces $M^5 \subset \mathbb{C}^3$ and discovered that they are all biholomorphic to tubes $S^2 \times i \mathbb{R}^3$ over some affinely homogeneous…
This paper present homogeneous CR hypersurfaces satisfying the $CR$-invariant property of being $k$-nondegenerate for an arbitrary integer $k\geq 1$. The construction of such homogeneous manifolds are based on $CR$ algebras defined by…
We determine all affinely homogeneous hypersurfaces S^3 in R^4 whose Hessian is (invariantly) of constant rank 2, including the simply transitive ones. We find 34 inequivalent terminal branches yielding each to a nonempty moduli space of…
We construct complete normal forms for $5$-dimensional real hypersurfaces in $\mathbb C^3$ which are $2$-nondegenerate and also of Levi non-uniform rank zero at the origin point ${\bf p} =0$. The latter condition means that the rank of the…
Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie…
We give a complete classification of polynomial models for smooth real hypersurfaces of finite Catlin multitype in $\mathbb C^3$, which admit nonlinear infinitesimal CR automorphisms. As a consequence, we obtain a sharp 1-jet determination…
A Levi nondegenerate real analytic hypersurface M of C^2 represented in local coordinates (z, w) in C^2 by a complex defining equation of the form w = Theta (z, \bar z, \bar w) which satisfies an appropriate reality condition, is spherical…
We study real-analytic Levi degenerate hypersurfaces M in complex manifolds of dimension 3, for which the CR-automorphism group Aut(M) is a real Lie group acting transitively on M. We provide large classes of examples for such M, compute…