Related papers: Remarks on Contact and Jacobi Geometry
Based on ideas of W. M. Tulczyjew, a geometric framework for a frame-independent formulation of different problems in analytical mechanics is developed. In this approach affine bundles replace vector bundles of the standard description and…
In this thesis we revise the concept of phase space in modern physics and devise a way to explicitly incorporate physical dimension into geometric mechanics. A historical account of metrology and phase space is given to illustrate the…
A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to…
We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and…
In this paper, we study the underlying geometry in the classical Hamilton-Jacobi equation. The proposed formalism is also valid for nonholonomic systems. We first introduce the essential geometric ingredients: a vector bundle, a linear…
We present the notion of higher Kirillov brackets on the sections of an even line bundle over a supermanifold. When the line bundle is trivial we shall speak of higher Jacobi brackets. These brackets are understood furnishing the module of…
Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic…
We show that a suitable notion of Dirac-Jacobi structure on a generic line bundle $L$, is provided by Dirac structures in the omni-Lie algebroid of $L$. Dirac-Jacobi structures on line bundles generalize Wade's $\mathcal E^1 (M)$-Dirac…
In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for different geometric structures attending to one particular…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
In this paper, for a Jacobi algebroid $A$, by introducing the notion of Jacobi quasi-Nijenhuis algebroids, which is a generalization of Poisson quasi-Nijenhuis manifolds introduced by Sti\'{e}non and Xu, we study generalized complex…
In this paper, we introduce a geometric structure called top, which is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of 1-forms (e.g. of contact and integrable forms) with…
We continue the study of compact holomorphic $p$-contact manifolds $X$ that we introduced recently by expanding the discussion to include non-K\"ahler hyperbolicity issues and a differential calculus based on what we call the Lie derivative…
Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a…
k-Contact geometry is a generalisation of contact geometry to analyse field theories. We develop an approach to k-contact geometry based on distributions that are distributionally maximally non-integrable and admit, locally, k commuting…
In this paper we introduce a generalization of Hamiltonian mechanics that replaces configuration spaces, conventionally regarded simply as smooth manifolds, with line bundles over smooth manifolds. Classical observables are then identified…
Let G be a Lie group endowed with a bi-invariant pseudo-Riemannian metric. Then the moduli space of flat connections on a principal G-bundle, P\to \Sigma, over a compact oriented surface, \Sigma, carries a Poisson structure. If we…
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…
Using the idea of a generalized Kaehler structure, which is a pair of commuting generalized complex structures, we construct bihermitian metrics on the projective plane and the product of two projective lines, and show that any such…
The notion of a Jacobi manifold is a natural generalization of that of a Poisson manifold. A Jacobi manifold has a natural foliation in which each leaf has either a contact structure or a locally conformal symplectic structure. In this…