Related papers: Holomorphic Extension from Weakly Pseudoconcave CR…

Let $M^n$ be a complete noncompact K$\ddot{a}$hler manifold of complex dimension $n$ with nonnegative holomorphic bisectional curvature. Denote by $\mathcal{O}$$_d(M^n)$ the space of holomorphic functions of polynomial growth of degree at…

This is the very first paper to focus on the CR analogue of Yau's uniformization conjecture in a complete noncompact pseudohermitian $(2n+1)$-manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of…

We give a solution to the equivalence and the embedding problems for smooth CR-submanifolds of complex spaces (and, more generally, for abstract CR-manifolds) in terms of complete differential systems in jet bundles satisfied by all…

In [21], the authors initiated the study of quasi generalized CR (QGCR)-null submanifolds. In this paper, attention is drawn to some distributions on ascreen QGCR-null submanifolds in an indefinite nearly cosymplectic manifold. We…

Let M of real dimension 2n-1 be a compact, orientable, weakly pseudoconvex manifold of dimension at least five, embedded in C^N (n less than or equal to N), of codimension one or more in C^N, and endowed with the induced CR structure. We…

For compact K\"ahlerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry…

In this paper, we consider the boundary M of a weakly pseudoconvex domain in a Stein manifold. We point out a striking difference between the local cohomology and the global cohomology of M, and illustrate this with an example. We also…

We study a germ of real analytic n-dimensional submanifold of $C^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck transformations,…

Let $D_j\subset\Bbb C^{n_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluriregular set, $j=1,...,N$. Put $$ X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times ...\times A_N\subset\Bbb…

In this article, we consider a complete, non-compact almost Hermitian manifold whose curvature is asymptotic to that of the complex hyperbolic plane. Under natural geometric conditions, we show that such a manifold arises as the interior of…

In this paper, we show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative pseudohermitian bisectional curvature with the CR maximal volume growth property.…

We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin$^{c, r}$ structure carrying a…

Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in…

For a smooth, non-degenerate locally integrable structure of hypersurface type on a manifold $M$, we provide necessary and sufficient conditions for it to be equivalent, near a point, to a real-analytic locally integrable structure (the…

We define a new local invariant (called degeneracy) associated to a triple (M,M',H), where M and M' are real submanifolds of C^N and C^N', respectively, and H: M->M' is either a holomorphic map, a formal holomorphic map, or a smooth CR-map.…

The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the…

Let $\Omega\subset\mathbb{C}^n$, $n\geq 2$, be a domain with smooth connected boundary. If $\Omega$ is relatively compact, the Hartogs-Bochner theorem ensures that every CR distribution on $\partial\Omega$ has a holomorphic extension to…

A CR manifold $M$, with CR distribution $\mathcal D^{10}\subset T^\mathbb C M$, is called {\it totally nondegenerate of depth $\mu$} if: (a) the complex tangent space $T^\mathbb C M$ is generated by all complex vector fields that might be…

We consider smooth deformations of the $CR$ structure of a smooth $2$-pseudoconcave compact $CR$ submanifold $\textsf{M}$ of a reduced complex analytic variety $\textsf{X}$ outside the intersection $D\,{\cap}\,\textsf{M}$ with the support…

We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or…