Related papers: The structure of CR manifolds

We study the pseudohermitian sectional curvature of a CR manifold.

We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a…

We give a proof of the regularity of Holder CR homeomorphisms of strictly pseudo convex CR manifolds of higher codimension.

We discuss various analytical and geometrical aspects of the Levi form, which is associated with a CR manifold having any CR dimension and any CR codimension.

In this paper, we deal with a strongly pseudoconvex almost CR manifold with a CR contraction. We will prove that the stable manifold of the CR contaction is CR equivalent to the Heisenberg group model.

Let $M^{2n+1}$, $n\ge 1$, be a smooth manifold with a pseudo-convex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $ M=\mathcal S_0 \supset \mathcal S_1 \supset \cdots \supset \mathcal S_{n}, $…

In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond…

We investigate the structure of real hypersurfaces with isometric Reeb flow in Kaehler manifolds. As an application we classify real hypersurfaces with isometric Reeb flow in irreducible Hermitian symmetric spaces of compact type.

We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotiens…

On a compact strictly pseudoconvex CR manifold $(M,\th)$, we consider the CR Yamabe constant of its infinite conformal covering. By using the maximum principles, we then prove a uniqueness theorem for the CR Yamabe flow on a complete…

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 show that biholomorphic automorphisms of a real analytic CR manifold can be considered as (pointwise) Lie symmetries of a holomorphic second order PDE system defining its Segre family. This allows to use general methods of the geometric…

The CR Yamabe constant is an invariant of a compact strongly pseudoconvex CR manifold and plays an important role in CR geometry. We show some integral formulae of the CR Yamabe constant. We also construct an infinite-dimensional family of…

The present paper deals with the study of pseudo parallel (in the sense of Chaki and in the sense of Deszcz) contact CR-submanifolds with respect to Levi-Civita connection as well as semisymmetric metric connection of Kenmotsu manifolds and…

We study stability properties of the topological entropy of Reeb flows on contact 3-manifolds with respect to the C^0-distance on the space of contact forms. Our main results show that a C^\infty-generic contact form on a closed co-oriented…

Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E.

R-circles in general three dimensional CR manifolds (of contact type) are the analogues to traces of Lagrangian totally geodesic planes on the sphere viewed as the boundary of two dimensional complex hyperbolic space. They form a family of…

The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples…

We show that the vanishing of the higher dimensional homology groups of a manifold ensures that every almost CR structure of codimension $k$ may be homotoped to a CR structure. This result is proved by adapting a method due to Haefliger…

In this paper we define the torsion flow, a CR analogue of the Ricci flow. For homogeneous CR manifolds we give explicit solutions to the torsion flow illustrating various kinds of behavior. We also derive monotonicity formulas for CR…