Related papers: Open Book Structures on Moment-Angle Manifolds $Z^…

Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…

We study a coverings of open books and virtually overtwisted contact manifolds using open book foliations. We show that open book coverings produces interesting examples such as transverse knots with depth grater than 1. We also demonstrate…

The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-manifolds admit a contact structure in every…

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact…

In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold $M$ is shown to be equivalent to existence of an ample $S^1$-invariant…

We relate open book decompositions of a 4-manifold M with its Engel structures. Our main result is, given an open book decomposition of M whose binding is a collection of 2-tori and whose monodromy preserves a framing of a page, the…

If a contact form on a (2n+1)-dimensional closed contact manifold admits closed Reeb orbits, then its systolic ration is defined to be the quotient of (n+1)th power of the shortest period of Reeb orbits by the contact volume. We prove that…

In this paper we study slant submanifolds of Lorentzian almost contact manifolds. We have taken the submanifold as a space like and then defined the slant angle on a submanifold and thus we extended the results of A. Lotta (Slant…

Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…

We describe explicit horizontal open books on some Seifert fibered 3--manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams…

We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

We generalise the theories of cosymplectic, contact, and cocontact manifolds to the infinite-dimensional setting and calculate model examples of time-dependent and dissipative Hamiltonian systems.

Some geometric structures with associated Riemannian metrics have been considered in the book.

In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that…

We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition…

We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…

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…

Riemannian metrics of positive Ricci curvature were constructed on certain moment-angle manifolds.