Related papers: Contact Dynamics versus Legendrian and Lagrangian …

It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-struc\-ture so that an almost contact metric structure and two almost contact B-metric structures are generated. There are…

In this article we construct and discuss a new rigorous geometric formalism for gauge field theories. The basis of our work is the notion of the Tulczyjew triple, a geometric structure which successfully solved numerous problems in…

Links in $S^3$ can be encoded by grid diagrams; a grid diagram is a collection of points on a toroidal grid such that each row and column of the grid contains exactly two points. Grid diagrams can be reinterpreted as front projections of…

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…

Let $\Lambda$ be a link of Legendrian spheres in the boundary of a subcritical $2n$-dimensional Weinstein manifold $X$. We show that, under some geometrical assumptions, the computation of the Legendrian contact homology of $\Lambda$ can be…

We provide a classification of $ts$-invariant sub-Lorentzian structures on $3$ dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for…

We study the geography of bilinearized Legendrian contact homology for closed, connected Legendrian submanifolds with vanishing Maslov class in 1-jet spaces. We show that this invariant detects whether the two augmentations used to define…

We show that the germ of the contact structure surrounding a certain kind of convex hypersurfaces is overtwisted. We then find such hypersurfaces close to any plastikstufe with toric core so that these imply overtwistedness. All proofs in…

Take a sequence of contactomorphisms of a contact three-manifold that $C^0$-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is Legendrian. We prove this by…

In this paper a symplectic realization for the Maxwell-Bloch equations with the rotating wave approximation is given, which also leads to a Lagrangian formulation. We show how Lie point symmetries generate a third constant of motion for the…

This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The previous paper in the series, math.DG/0008155, defined the idea of evolution data, which includes an (m-1)-submanifold P…

We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair $(X,L)$ consisting of an exact symplectic manifold $X$ and an exact…

This paper introduces two constructions of Legendrian submanifolds, called the Legendrian product and spinning, and computes their classical invariants, the Thurston-Bennequin invariant and the Maslov class, in R^{2n+1}. These constructions…

Unit tangent bundles $UM$ of semi-Riemannian manifolds $M$ are shown to be examples of dynamical Legendrian contact structures, which were defined in recent work [25] of Sykes-Zelenko to generalize leaf spaces of 2-nondegenerate CR…

Complex contact manifolds have recently received considerable attention. Many of the newer publications approach contact manifolds via the covering family of minimal rational curves. This short note furthers the study of these curves. It is…

We construct special Lagrangian submanifolds of the Taub-NUT manifold and the Atiyah-Hitchin manifold by combining the generalized Legendre transform approach and the moment map technique. The generalized Legendre transform approach…

Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transformations with four- and five-dimensional Lie symmetry algebras,…

In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the…

In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions…