Related papers: Bi-Legendrian manifolds and paracontact geometry

Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.

In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…

For any knot T transverse to a given contact structure on a 3-manifold, we exhibit a Legendrian two-component link such that T equals the transverse push-off of one of the link components and contact (+1)-surgery on the link has the same…

In this study, we introduce indefinite sasakian statistical manifolds and lightlike hypersurfaces of an indefinite sasakian statistical manifold. Some relations among induced geometrical objects with respect to dual connections in a…

We give a procedure to ``average'' canonically $C^1$-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves a Legendrian submanifold almost invariant, there is an invariant…

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

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds…

We define relative versions of the classical invariants of Legendrian and transverse knots in contact 3-manifolds for knots that are homologous to a fixed reference knot. We show these invariants are well-defined and give some basic…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

Almost paracontact Riemannian manifolds of the lowest dimension are studied, whose paracontact distributions are equipped with an almost paracomplex structure. These manifolds are constructed as a product of a real line and a 2-dimensional…

Lagrangian formalism on graded manifolds is phrased in terms of the Grassmann-graded variational bicomplex, generalizing the familiar variational bicomplex for even Lagrangian systems on fiber bundles.

In this article, we investigate the Riemannian and semi-Riemannian metrics on the base space of the Boothby-Wang fibration of a closed regular non-Sasakian $(\kappa, \mu)$-manifold. To this end, we study a natural class of deviations of the…

We study holomorphic Legendrian curves in the standard complex contact structure on the projectivised cotangent bundle $X=\mathbb P(T^*Z)$ of a complex manifold $Z$ of dimension at least $2$. We provide a detailed analysis of Legendrian…

We consider a bi-Lagrangian structure $(\omega,\mathcal{F}_{1},\mathcal{F}_{2})$ on a manifold $M$, that is, $(M,\omega,\mathcal{F}_{1},\mathcal{F}_{2})$ is a bi-Lagrangian manifold. We prolong bi-Lagrangian structures on $M$, and lift a…

We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard or generalized entropies. For this purpose, we introduce dualistic structure defined by information geometry, and…

We make a case for the unique relevance of Cartan geometry for gauge theories of gravity and supergravity. We introduce our discussion by recapitulating historical threads, providing motivations. In a first part we review the geometry of…

In this study, taking into considering lifting theory, we shall obtain both almost complex and paracomplex structures on the tangent bun- dle, based on almost Lorentzian r-contact and r-paracontact manifold.

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure.…