arXiv research

Study explores weak generalized K-contact structures in contact metric spaces.

Defines generalized Sasakian structures in contact geometry.

Established a generalized Boothby-Wang theorem in contact geometry.

Study new $k$-contact distributions and Lie systems.

Study on generalized quasi-Einstein structures in contact geometry.

Abstract: Survey on contact submanifolds.

Proposes a contact dynamics framework using generalized geometries.

Lie contact structures generalize the classical Lie sphere geometry of oriented hyperspheres in the standard sphere. They can be equivalently described as parabolic geometries corresponding to the contact grading of orthogonal real Lie algebra. It follows the underlying geometric structure can be interpreted in several…

Discusses the tight versus overtwisted dichotomy in 3D contact geometry.

Spinors help study unique five-dimensional contact structures.

In this paper we generalize the main notions from the geometry of (almost) contact manifolds in the category of Lie algebroids. Also, using the framework of generalized geometry, we obtain an (almost) contact Riemannian Lie algebroid structure on a vertical Liouville distribution over the big-tangent manifold of a Riem…

The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of d…

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

Infinite-dimensional contact geometry explored.

New surgery method preserves Anosov flow properties using bi-contact geometry.

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

A new method simplifies contact Hamiltonian mechanics.

Develops k-contact geometry theory for field theories.

Characterizes Anosov flows in 3D using symplectic and contact geometry.

A dictionary connects symplectic to contact geometry, with applications to complex and G-structures.

Study local geometry of bi-contact structures on 3-manifolds.

Local flatness theorem for paraquaternionic contact structures.

In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermitian almost contact metric spac…

Paper explores existence and nonexistence of submanifolds in contact geometry.

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

Study non-squeezing phenomena in contact geometry using specific capacities.

A PhD thesis written under supervision of Pawel Nurowski and defended at the Faculty of Physics of the University of Warsaw. We adress the problems of local equivalence and geometry of third order ODEs modulo contact, point and fibre-preserving transformations of variables. Several new and already known geometries are …

Introduces pqc structures, generalizing para 3-Sasakian geometry.

On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry o…

This article sketches various ideas in contact geometry that have become useful in low-dimensional topology. Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact structures, (2) discuss Eliashberg and Weinstein's symplectic handle attachments, an…

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

We prove, for a class of contact manifolds, that the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to invariants of contactomorphisms which generalize the classical notion of the rotation …

New Skyrme model for contact geometry with topological solutions.

Simplified construction of contact triad connection for analysis.

We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampere (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalence method to study the gen…

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…

In this paper, the notion of an almost contact Kählerian structure is introduced. The interior geometry of almost contact Kählerian spaces is investigated. On the zero-curvature distribution of an almost contact metric structure, as on the total space of a vector bundle, an almost contact Kählerian structure is obtaine…

Contact reductions explained through symplectic reductions.

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…

This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact geometry. Specifically, if a given three dimensional contact manifold (M,ξ) admits a …

Generalizes surgery techniques for projectively Anosov flows.

Characterizes Anosov flows via contact geometry.

A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of …

Complex contact manifolds arise naturally in differential geometry, algebraic geometry and exterior differential systems. Their classification would answer an important question about holonomy groups. The geometry of such manifold $X$ is governed by the contact lines contained in $X$. These are related to the notion of…

Study on null submanifolds in indefinite complex contact geometry.

We study the geometry of the cuspidal edge $M$ in $\mathbb R^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$. We classify submersions on a model of $M$ by diffeomorphisms and recover the cont…

Study new warped product metric in contact geometry.

New systems of linear PDEs discovered in 3D contact manifolds.