Related papers: Contact structures on algebraic 5-dimensional mani…

In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular…

We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on…

In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not contact isotopic. This is the first example of rigidity for…

In this paper, we write down Seiberg-Witten equations on contact metric manifolds of dimension 5. Any contact metric manifold has a spin^c structure. For Dirac equation we use Dirac type operators associated to the generalized…

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with…

A geometric obstruction, the so called "plastikstufe", for a contact structure to not being fillable has been found by K. Niederkruger. This generalizes somehow the concept of overtwisted structure to dimensions higher than 3. This paper…

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit a semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable…

In this article we conjecture a 4-dimensional characterization of tightness: a contact structure is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in Yx[0,1]. An affirmative answer to our conjecture…

We establish a relation between higher contact-like structures on supermanifolds and the N = 1 super-Poincare group via its superspace realisation. To do this we introduce a vector-valued contact structure, which we refer to as a…

We show that every closed toroidal irreducible orientable 3-manifold carries infinitely many universally tight contact structures.

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic…

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic…

We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact…

Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated.

We prove the existence of essential loops in the space of contact structures on torus bundles over the circle.

In this paper, we study the global behaviour of contact structures on oriented manifolds V which are circle bundles over a closed orientable surface S of genus g>0. We establish in particular contact analogs of a number of classical results…

We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are…

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many…

In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5.