arXiv research

Study new warped product metric in contact geometry.

The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.

The paper studies regular contact manifolds and their products.

Paper explores existence and nonexistence of submanifolds in contact geometry.

B.-Y. Chen initiated the study of warped product submanifolds in his fundamental seminal papers \cite{C1,C2,C2.1}. In this paper, we study contact CR-warped product submanifolds of cosymplectic space forms and prove an optimal inequality by using Gauss and Codazzi equations. In addition, we obtain two geometric inequal…

Constructs non-unital monoidal category of contact manifolds and Legendrian correspondence calculus

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product cont…

Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a decomposition as required for (i) for all closed, oriented 4-manifolds. As a corollary, w…

In this paper we address what generalized geometric structures are possible on products of spaces that each admit generalized geometries. In particular we consider, first, the product of two odd dimensional spaces that each admit a generalized almost contact structure, and then subsequently, the product of an odd dimen…

In this paper, we study warped products of contact skew-CR submanifolds, called contact skew CR-warped products. We establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. The equality case in the statement of the inequality is investigated and s…

Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular…

The study examines conditions for weak nearly cosymplectic manifolds to split into products.

Researchers extend Godbillon-Vey functional to almost contact manifolds, finding critical structures.

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no pr…

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally we give examples.

We employ cut and paste contact topological techniques to classify some tight contact structures on the closed, oriented genus-2 surface times the interval. A boundary condition is specified so that the Euler class of the of the contact structure vanishes when evaluated on each boundary component. We prove that there e…

We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto's Theorem on product of almost contact manifolds to flat bundles. We construct som…

The paper derives inequalities for contact CR-warped product submanifolds in cosymplectic space forms.

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of almost contact metric warped products are also studied, relating their harmonic…

We construct a compact simply-connected 7-dimensional manifold admitting a K-contact structure but not a Sasakian structure. We also study rational homotopy properties of such manifolds, proving in particular that a simply-connected 7-dimensional Sasakian manifold has vanishing cup-product on the second cohomology and …

Study shows magnetic trajectories in Berger spheres are homogeneous.

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…

In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We in…

Legendrian contact homology (LCH) and its associated differential graded algebra are powerful non-classical invariants of Legendrian knots. Linearization makes the LCH computationally tractable at the expense of discarding nonlinear (and noncommutative) information. To recover some of the nonlinear information while pr…

We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed orientable irreducible 3-manifold M with nonzero second homol-ogy carries a hyperti…

The object of investigations are almost contact B-metric manifolds which are derived as a product of a real line and a 2-dimensional manifold equipped with a complex structure and a Norden metric. There are used two different methods for generation of the B-metric on the product manifold. The constructed manifolds are …

In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if $M = N^{\perp} \times_f N^T$ is a warped CR-submanifold such that $N^{\perp}$ is $φ$?-anti-invariant and NT is $φ$?-invariant, then M is a CR-product. We…

The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.

New contact structures extend supergravity solutions.

We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact manifolds not locally quaternionic contact conformal to the quaternionic sphere. W…

Extends Sasakian structures to arbitrary contact manifolds.

In this note, we use the recent work of Honda-Kazez-Matic [HKM] to prove that a closed contact 3-manifold admitting a compatible open book decomposition with a nontrivial monodromy which can be presented as a product of left handed Dehn twists is overtwisted.

We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the once-punctured torus. Given such a product, we supply an algorithm to determine whether the …

We show that $φ$-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least $2$ are all minimal. We prove that an odd-dimensional $φ$-invariant submanifold …

Mean curvature flow converges to a translating soliton with prescribed contact angle.

The study explores $(m,ρ)$-quasi-Einstein structures on contact metric manifolds.

In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the implications of this theorem with regard to the definition of generalized Sasakian and ge…

The paper studies special contact metric manifolds and their properties.

Homogeneous magnetic trajectories in a special linear group proven.

Proves Weinstein's and Arnold's conjectures using contact instantons.

We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold is a Calabi-Eckmann manifold. Moreover we show that a complete, simply connected, normal metric contact pair manifold such that the foliation induced by the vertical subbundle is regular and reflections in the integ…

Proves Giroux Correspondence in 3D using Heegaard splittings.

In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered sutured Floer theory. Being isomorphic to the homology of a differential graded algebra, this contact category algebra has an A-infinity structure, allowing us to comb…

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 generalizes the standard notion of open book decomposition and allows one to mo…

There are considered 4-dimensional pseudo-Riemannian spaces with inner products of signature (3,1) and (2,2). The objects of investigation are space-like and time-like hyperspheres in the respective cases. These hypersurfaces are equipped with almost contact B-metric structures. The constructed manifolds are characteri…

We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 …

Study confoliations' symplectic fillability, finding obstructions.

Recently Hui et al. (\cite{HAP}, \cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not ex…