Related papers: Diffeomorphisms preserving R-circles in three dime…

Given the interest in relating the large $N$ limit of SU(N) to groups of area-preserving diffeomorphisms, we consider the topologies of these groups and show that both in terms of homology and homotopy, they are extremely different. Similar…

We provide a new angle and obtain new results on a class of metrics on length-normalized curves in $d$ dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the…

A surface in the 4-sphere is trivially embedded, if it bounds a 3-dimensional handle body in the 4-sphere. For a surface trivially embedded in the 4-sphere, a diffeomorphism over this surface is extensible if and only if this preserves the…

Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…

The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…

Consider a holomorphic contact manifold. Holomorphic discs tangent to the contact planes define a pseudometric on the manifold. This pseudometric integrates to a pseudodistance. When the pseudodistance is a distance, we call the contact…

We define flag structures on a real three manifold M as the choice of two complex lines on the complexified tangent space at each point of M. We suppose that the plane field defined by the complex lines is a contact plane and construct an…

This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal…

We characterize homogeneous three-dimensional CR manifolds, in particular Rossi spheres, as critical points of a certain energy functional that depends on the Webster curvature and torsion of the pseudohermitian structure.

Let $A$ be a H\"older continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold $M$. We consider the periodic data of $A$, i.e., the set of its return values along the periodic…

A closed manifold is called a biquotient if it is diffeomorphic to K\G/H for some compact Lie group G with closed subgroups K and H such that K acts freely on G/H. Biquotients are a major source of examples of Riemannian manifolds with…

Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism.

In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism…

We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

In the present paper we consider preserving orientation Morse-Smale diffeomorphisms on surfaces. Using the methods of factorization and linearizing neighborhoods we prove that such diffeomorphisms have a finite number of orientable…

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…

We consider the class of diffeomorphisms of a manifold that its differential keeps invariant a one-dimensional subbundle $E$. For that type of diffeomorphisms is naturally defined a one-parameter family called $E-$translation. We prove that…

We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces…

We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove…

A contact form is called K-contact if its Reeb vector field is Killing with respect to some Riemannian metric. In this paper we classify K-contact forms whose Reeb vector field admits at least one non-periodic orbit, on three-dimensional…