Related papers: Geometry of jet spaces and integrable systems
A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…
This paper is the sequel to our previous paper (Differetial Geometry of Microlinear Frolicher spaces IV-1), where three approaches to jet bundles are presented and compared. The first objective in this paper is to give the affine bundle…
Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations…
In this research oriented manuscript, foundational aspects of rigid geometry are discussed, putting emphasis on birational side of formal schemes and topological feature of rigid spaces. Besides the rigid geometry itself, topics include the…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence…
These notes provide an introduction to the algebra and geometry of differential operators and jet bundles. Their point of view is guided by the leitmotiv that higher-spin gravity theories call for higher-order generalisations of Lie…
In this talk the description of gauge theories associated with internal symmetries is extended to the case in which the symmetry group is the space-time translation group (recovering Einstein's theory) using the standard jet-bundle…
We establish an in-in formalism for geodesic deviation as an alternative to Synge calculus, based on a covariant calculus of differential forms in tangent bundle. This derives the exact Lagrangian and equations governing the finite geodesic…
In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold for jet bundles on projective space in any dimension. We also…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
This paper concerns the model theory of jet spaces (i.e., higher-order tangent spaces) in differentially closed fields. Suppose p is the generic type of the jet space to a finite dimensional differential-algebraic variety at a generic…
The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the…
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…
We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gr\"obner bases to clarify crucial notions concerning compatibility…
Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic…