Related papers: Horizontal Path Lifting for General Connections
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.
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…
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 address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…
The paper is devoted to introduce some notions extending the unique path lifting property from a homotopy viewpoint and to study their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…
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…
Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case…
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…
For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on…
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 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…
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…
We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence…
I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.
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.
This work revisits, from a geometric perspective, the notion of discrete connection on a principal bundle, introduced by M. Leok, J. Marsden and A. Weinstein. It provides precise definitions of discrete connection, discrete connection form…