相关论文: A note on jet and geometric approach to higher ord…
Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…
In this review paper we discuss the different interpretations of the concept of connection in a fiber bundle and in a jet bundle, and relate it with first and second-order systems of partial differential equations (PDE's) and multivector…
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
In this paper we will be considering a basic geometric problem, the extension problem of classical Hamilton-Cartan variational theory to higher jet prolongations on fibered manifolds.
This note is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of…
We define and study jets of flat partial connections with respect to singular foliations. In particular, we use the first sheaf of transverse jets to address the problem of extending a flat partial connection to a (flat) meromorphic…
In this paper we define $n$th order Hessian structures on manifolds and study them. In particular, when $n = 3$, we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it…
We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables,…
The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…
We define and study jets of flat partial connections in the setting of smooth foliations and flat partial connections on locally free sheaves. In the case of codimension one foliations, we apply this definition to characterize transversely…
Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…
Jet classification in high-energy particle physics is important for understanding fundamental interactions and probing phenomena beyond the Standard Model. Jets originate from the fragmentation and hadronization of quarks and gluons, and…
It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry.
We prove that, in the setting of noncommutative differential geometry, a system of higher order connections is equivalent to a suitable generalization of the notion of phase space quantization (in the sense of Moyal star products on the…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
Jets of mappings introduced by Ehresmann are still the most useful objects for formulating geometric frameworks of physical theories. We are proposing modifications designed to make jet theory less dependent on local coordinates. Extensions…
The jet shape is a simple measure of how widely a jet's energy is spread. At present jet shape distributions have only been calculated to leading order in perturbative QCD. In this paper we consider how much these predictions should be…
Jets frames, that is a generalisation of ordinary frames on a manifold, are described in a language similar to that of gauge theory. This is achieved by constructing the Cartan geometry of a manifold with respect to the diffeomorphism…