arXiv research

Regular Jacobi structures on line bundles lead to generalized contact bundles.

Study of local structure of generalized contact bundles.

Generalizes Tulczyjew triples for contact manifolds in Hamiltonian and Lagrangian formalisms.

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 construction of K-contact manifolds generalizing Yamazaki's fiber join construction and a…

New systolic inequality for 3D contact forms on Seifert bundles.

A connected Fano complex-contact manifold is isomorphic to the kaehlerian C-space of Boothby type with a natural complex-contact structure corresponding to a non-abelian simple complex Lie algebra if the contact line bundle is very ample. A. Beauville relaxed the provision to two assumptions that the contact line bundl…

Introduces contact dual pairs using line bundles.

The paper defines a new structure on tangent sphere bundles and characterizes their properties.

The paper studies regular contact manifolds and their products.

A new method simplifies contact Hamiltonian mechanics.

Study contact geometry of symplectic divisors, invariant under specific transformations.

We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an invariant contact structure, only provided the trivial bundle does. In particul…

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of the integrability condition for generalized contact structures; (3) in light of ne…

Study of Pascal algebra matrices and their jet bundle map for vector bundles.

A contact metric manifold is said to be $H$-contact, if the characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold $M$ equipped with the standard contact metric structure is $H$-contact if and only if $M$ is $2$-stein.

This thesis extends contact structures to differentiable stacks using line bundle-valued 1-forms.

Study harmonicity of normal almost contact structures on Riemannian manifolds.

We study the contact equivalence problem for toric contact structures on $S^3$-bundles over $S^2$. That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To f…

Embeds all contact 3-manifolds into specific 5-manifolds.

Study on Klein bottle's cotangent bundle using contact homology.

Sharp systolic inequality for invariant tight contact forms on S1-bundles over S2.

In this paper, we study strong symplectic fillability and Stein fillability of some tight contact structures on negative parabolic and negative hyperbolic torus bundles over the circle. For the universally tight contact structure with twisting $π$ in $S^1$-direction on a negative parabolic torus bundle, we completely d…

In this paper, we compute contact homology of some quasi-regular contact structures, which admit Hamiltonian actions of Reeb type of Lie groups. We will discuss the toric contact case, (where the torus is of Reeb type), and the case of homogeneous contact manifolds. In both of these cases the quotients by the Reeb acti…

Characterizes invariant contact metric structures on tangent sphere bundles of compact symmetric spaces.

The paper explores CR structures and their leaf spaces in semi-Riemannian manifolds.

The paper defines and proves equivalence of nonholonomic brackets in contact mechanical systems.

The paper proves stability for contact groupoids and deformations.

Study geometric structures on twistor and reflector spaces of paraquaternionic contact manifolds.

We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact structures from a counterpart of generalized complex structures on odd-dimensiona…

Study properties of contact structures on symplectic disk bundles with concave boundaries.

We develop a systematic approach to contact and Jacobi structures on graded supermanifolds. In this framework, contact structures are interpreted as symplectic principal GL(1,R)-bundles. Gradings compatible with the GL(1,R)-action lead to the concept of a graded contact manifold, in particular a linear (more generally,…

We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a compact surface.

Study connects contact structures to cone geodesics and contactomorphisms.

Stein and Weinstein structures are described for disk cotangent bundles of surfaces.

If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form which linearly deforms into contact forms, then M supports a K-contact form. On the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if and only if it is a fibration 1-form. on any other 2-torus bundle over the circle, ev…

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

Develop contact Tulczyjew formalism for dissipative dynamics on skew algebroids.

We extend the theorems concerning the equivariant symplectic reduction of the cotangent bundle to contact geometry. The role of the cotangent bundle is taken by the cosphere bundle. We use Albert's method for reduction at zero and Willett's method for non-zero reduction. We provide examples for both cases.

Jet bundles as higher-order polarised $k$-contact manifolds

Established a generalized Boothby-Wang theorem in contact geometry.

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…

We study weak versus strong symplectic fillability of some tight contact structures on torus bundles over the circle. In particular, we prove that almost all of these tight contact structures are weakly, but not strongly symplectically fillable. For the 3-torus this theorem was established by Eliashberg.

Extending our earlier results, we prove that certain tight contact structures on circle bundles over surfaces are not symplectically semi--fillable, thus confirming a conjecture of Ko Honda.

We classify locally the contact metric (k,mu)-spaces whose Boeckx invariant is $\le -1$ as tangent hyperquadric bundles of Lorentzian space forms.

Develops k-contact geometry theory for field theories.

The paper reformulates Legendrian contact homology using string topology.

We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS's. In particular, we generaliz…