Related papers: Geometry of jet spaces and integrable systems
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
In this paper, we expand on previous work describing partial derivatives and metric component estimators to define tangent spaces on causal sets. Partial derivative operators are the basis vectors of the tangent space, and the metric…
Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…
In this article, we treat G_2-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G_2-structure; in…
The book can be divided in three parts: the Lagrange geometry of order $k$, presented in the first three chapters, the geometrical theory of the dual manifolds $T^{*k}M$ - chapters 4-7 and the geometry of Hamilton spaces of order $k$ and…
In the context of generalized geometry we first show how the Courant bracket helps to define connections with skew torsion and then investigate a five-dimensional invariant functional and its associated geometry. A Hamiltonian flow arising…
The phenomenology of jets associated with a variety of black hole systems is summarized, emphasizing the constraints imposed on their origin. Models of jet formation are reviewed, focusing in particular on recent ideas concerning MHD…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…
We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
A study of sigma models whose target space is a group G that admits a compatible Poisson structure is presented. The natural action of O(D,D;Z) on the generalised tangent bundle TG+T*G and a generalisation of the Courant bracket that…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
A notion of internal Lagrangian for a system of differential equations is introduced. A spectral sequence related to internal Lagrangians is obtained. A connection between internal Lagrangians and presymplectic structures is investigated.…
Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's equations, on the…
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given…
A brief overview of jets and their central drivers is presented, with a focus on accreting black hole systems. In particular, scaling relations that elucidate some basic properties of the engines are derived, and the implications for the…
L-Infinity structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of $L_n$ and $L_{\infty}$ structures on…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture…
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and…