Related papers: Tight Contact Structures on Lens Spaces
We prove the existence of essential loops in the space of contact structures on torus bundles over the circle.
We study the structures of arbitrary split Leibniz triple systems. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of $T$ being of maximal length, the simplicity of the…
We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on $S^3$ preserves a standard contact structure pointwise. We also relate univerally…
For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new…
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…
In this paper we study some affine structures on nilpotent Lie algebras endowed with a contact form. These affine structures are constructed from an affine structure on a symplectic Lie algebra by a central extension.
L-Infinity structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of $L_n$ and $L_{\infty}$ structures on…
Whether every hyperbolic 3-manifold admits a tight contact structure or not is an open question. Many hyperbolic 3-manifolds contain taut foliations and taut foliations can be perturbed to tight contact structures. The first examples of…
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…
The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the…
The description of point defects in chiral liquid crystals via topological methods requires the introduction of singular contact structures, a generalisation of regular contact structures where the plane field may have singularities at…
We prove that every homotopy class of almost contact structures on a closed 5-dimensional manifold admits a contact structure.
We give a complete proof of the fact that a contact structure that is sufficiently close to a Reebless foliation is universally tight.
We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds $N=M(D^{2}; r_1, r_2)$ with minimal convex boundary of slope $s$ and Giroux torsion 0 along $\partial N$, where $r_1,r_2\in…
Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…
We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
In the paper we prove, that extrinsic curvature does not impose restrictions on the topology of a contact structure, except the obvious ones.
We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun…
We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any…
A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for…