We survey some recent results on local geometric properties of real submanifolds of
complex space. Our main focus is on the structure and properties of mappings between such …

$2 $-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-
geometry and the theory of Hermitian Symmetric Domains. In this paper, we construct a …

Applying Lie's theory, we show that any $\mathcal {C}^\omega $ hypersurface $ M^
5\subset\mathbb {C}^ 3$ in the class $\mathfrak {C} _ {2, 1} $ carries Cartan-Moser chains of …

The general theory of parabolic geometries is applied to the study of the normal Cartan
connections for all hyperbolic and elliptic 6-dimensional CR-manifolds of codimension two …

We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-codimension 2
to parallelisms thus solving the problem of global equivalence for such manifolds. The …

We construct a complete convergent normal form for a real hypersurface in ℂ N, N≥ 2, at a
generic Levi-degeneracy. This seems to be the first convergent normal form for a Levi …

We study the holomorphic equivalence problem for finite type hypersurfaces in C 2. We
discover a geometric condition, which is sufficient for the existence of a natural convergent …

Normal forms in Cauchy-Riemann geometry Page 162 Contemporary Mathematics Volume
681 , 2017 http://dx. doi. org/10.1090/conm/681/13685 Normal forms in Cauchy-Riemann …

In the present paper we suggest an explicit construction of a Cartan connection for an elliptic
or hyperbolic CR manifold M of dimension six and codimension two, ie a pair (P, ω) …

Let X be a compact real (2n+ 2)-dimensional submanifold of the complex space Cn+ 2. For
generic such X at all but a finite number of points, the tangent space of X will have a 2n …