Related papers: Poisson fiber bundles and coupling Dirac structure…
We consider certain fiber bundles over a paraquaternionic contact manifolds, called twistor and reflector spaces, and show that these carry an intrinsic geometric structure that is always integrable.
This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we…
Many mechanical systems are large and complex, despite being composed of simple subsystems. In order to understand such large systems it is natural to tear the system into these subsystems. Conversely we must understand how to invert this…
We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible K\"ahler structure. The case of the unitary group allows us to reformulate the geometric framework of quantum information theory. In…
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…
The paper starts with an interpretation of the complete lift of a Poisson structure from a manifold M to its tangent bundle TM by means of the Schouten- Nijenhuis bracket of covariant symmetric tensor fields defined by the co- tangent Lie…
In this paper, we will give the polyhedron property role to satisfy fiber homotopically equivalent relation in fiber bundle theory over suspensions of polyhedron space.
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the…
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…
We study the band structures and the associated contact points for a phosphorene superlattice made up of two periodic areas. We use the boundary conditions to extract an equation describing the dispersion relation after obtaining the…
We extend a previously successful discussion of the constrained Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a…
A Dirac structure is a Lagrangian subbundle of a Courant algebroid, $L\subset\mathbb{E}$, which is involutive with respect to the Courant bracket. In particular, $L$ inherits the structure of a Lie algebroid. In this paper, we introduce the…
This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints. In particular, we clarify the geometric…
We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We…
In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the…
We prove an analogue of the Kobayashi-Hitchin correspondence oncompact connected 3-folds that is fibered on orbifold Riemann surfaces and satisfy an integrability condition, which contains compact connected Sasakian 3-folds. We define…
We study compatible contact structures of fibered Seifert multilinks in homology 3-spheres and especially give a necessary and sufficient condition for the contact structure to be tight in the case where the Seifert fibration is positively…
The main result of this paper is the construction of a family of superintegrable Hamiltonian systems on moduli spaces of flat connections on a principle $G$-bundle on a surface. The moduli space is a Poisson variety with Atiyah-Bott Poisson…
We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2…
We construct Poisson brackets at boundaries of open strings and membranes with constant background fields which are compatible with their boundary conditions. The boundary conditions are treated as primary constraints which give infinitely…