Related papers: Global CR functions on parabolic CR manifolds

We continue the analysis of definably compact groups definable in a real closed field $\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\mathcal{R}$ there are a connected…

Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality…

In this paper we shall give sufficient conditions for local CR diffeomorphisms between two real analytic submanifolds of $\Bbb C^N$ to be determined by finitely many derivatives at finitely many points. These conditions will also be shown…

In this paper, homology of a contact CR-submanifold of a real hypersurface, which has naturally almost contact metric structure induced from the complex Euclidean space $\mathbb{C}^{m}$, is examined. More precisely, nonexistence of stable…

Let ${\bold M}_0$ be a compact, regular q-pseudoconcave compact CR submanifold of a complex manifold ${\bold G}$ and ${\cal B}$ - a holomorphic vector bundle on ${\bold G}$ such that $\dim H^r({\bold M}_0, {\cal B}\big|_{\bold M})=0$ for…

We study the second fundamental form of semi-isometric CR immersions from strictly pseudoconvex CR manifolds into K\"ahler manifolds. As an application, we give a precise condition for the CR umbilicality of real hypersurfaces, extending an…

We apply the general theory of codimension one integrability conditions for $G$-structures developed in arXiv:1306.6817v3 [math.DG] to the case of quaternionic CR geometry. We obtain necessary and sufficient conditions for an almost CR…

Let $M$ be a compact connected pseudo-Riemannian manifold on which a solvable connected Lie group $G$ of isometries acts transitively. We show that $G$ acts almost freely on $M$ and that the metric on $M$ is induced by a bi-invariant…

Let $M \subset {\mathbb{C}}^{n+1}$, $n \geq 2$, be a real codimension two CR singular real-analytic submanifold that is nondegenerate and holomorphically flat. We prove that every real-analytic function on $M$ that is CR outside the CR…

Developing ideas of \cite{Fei}, we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold $M$. Graded…

The purpose of this paper is to study the canonical totally real foliations of CR-submanifolds in a locally conformal K\"{a}hler manifold.

Using functional analysis and a Friedrichs approximation lemma for first order differential operators, we derive a global homotopy formula in large degrees for the tangential Cauchy-Riemann operator from local homotopy formulas without loss…

Let $G_\mathbb{R}$ be a Lie group and $G$ its complexification. An open $G_\mathbb{R}$-orbit in a $G$-flag manifold is measurable whenever it carries a $G_\mathbb{R}$-invariant volume element. In this paper the notion of measurability is…

We study the action of a real reductive group $G$ on a real submanifold $X$ of a Kahler manifold $Z$. We suppose that the action of a compact connected Lie group $U$ with Lie algebra $\mathfrak{u}$ extends holomorphically to an action of…

In this paper, we show that the CR $Q$-curvature is orthogonal to the space of CR pluriharmonic functions on any closed strictly pseudoconvex CR manifold of dimension at least five. To this end, we obtain a cohomological expression of the…

For compact CR manifolds of hypersurface type which embed in complex projective space, we show that for all k large enough there exist linear systems of ${\mathcal{O}}(k)$ which when restricted to the CR manifold are generic in a suitable…

Let G be a semi-simple Lie group and Q a parabilic subgroup of its complexification G^\mathbb C, then Z:=G^\mathbb C/Q is a compact complex homogeneous manifold. Moreover, G as well as K^\mathbb C, the complexification of the maximal…

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…

We consider CR submersive mappings between generic submanifolds in complex space. We show that, under suitable conditions on the manifolds, there is an integer k such that any jet of the CR mapping at a given point is a rational function of…

Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M,g) of signature (p,q) on which G can act conformally. Precisely, we determine the smallest possible value for the index min(p,q) of the metric. When…