相关论文: Transports along maps in fibre bundles
The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths…
Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.
A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the…
The (parallel) linear transports along paths in vector bundles are axiomatically described. Their general form and certain properties are found. It is shown that these transports are locally (i.e. along every fixed path) always Euclidean…
The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…
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…
A generalised notion of connection on a fibre bundle E over a manifold M is presented. These connections are characterised by a smooth distribution on E which projects onto a (not necessarily integrable) distribution on M and which, in…
The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
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…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the…
Curvature and torsion of linear transports along paths in, respectively, vector bundles and the tangent bundle to a differentiable manifold are defined and certain their properties are derived.
We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…
The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric…
We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a…
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…