Related papers: Connections and jet fields
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet--like approach considers a higher order…
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\to E\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable connections in the bundle $E\to…
These Lectures summarize the relevant material on existent applications of jet manifold techniques to classical and quantum field theory. The following topics are included: 1. Fibre bundles, 2. Jet manifolds, 3. Connections, 4. Lagrangian…
In this note we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we…
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…
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…
The below discussion is in three sections A, B, C, each section in two parts I, II, I representing the standpoint of bundles with connections and II representing the standpoint of prehomogeneous geometries (phg's). In A, our object of study…
It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry.
The construction of a linear connection on a pullback bundle from a connection on a vector bundle is explained in terms of fiberwise linear approximation. This procedure clarifies the geometric meaning of the linearized connection as well…
Systems of partial differential equations lie at the heart of physics. Despite this, the general theory of these systems has remained rather obscure in comparison to numerical approaches such as finite element models and various other…
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional…
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.
We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as…
Tangent categories provide an axiomatic approach to key structural aspects of differential geometry that exist not only in the classical category of smooth manifolds but also in algebraic geometry, homological algebra, computer science, and…
The fibre bundle formulation of gauge theory is generally accepted. The jet manifold machinery completes this formulation and provides the adequate mathematical description of dynamics of fields represented by sections of fibre bundles.…
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…
This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.
The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.