2 Note on generalised connections and affine bundles
نویسنده
چکیده
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 affineness of a generalised connection.
منابع مشابه
The Berwald-type linearisation of generalised connections
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 connection of Berwald type in the standard theory of connections. Various new insights are being obtained in the fine structure of affine bundles over an anc...
متن کاملSimple Mechanical Control Systems with Constraints and Symmetry
We develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. Taking the viewpoint of affine connection control systems, we derive reduced formulations of the Levi-Civita and the nonholonomic affine connections, along with the symmetric product, in the presence of symmetries and nonholonomic constraint...
متن کاملGeneralised connections and curvature
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 generalised connection. Some applications to singular solutions of Yang-Mills theory are given. Mathematics Subject Classification (2000): Primary: 46T30; secondary...
متن کاملar X iv : h ep - t h / 03 10 02 0 v 1 2 O ct 2 00 3 MECHANICAL D BRANES AND B FIELDS
We represent B fields and higher p-form potentials on a manifold M as connections on affine bundles over M . We realize D branes on M as special submanifolds of these affine bundles. We check the physical relevance of this representation by showing that the properties of the resulting branes closely correspond to those of their string theory counterparts. As a simple application of this geometr...
متن کاملB Fields from a Luddite Perspective
In this talk, we discuss the geometric realization of B fields and higher p-form potentials on a manifold M as connections on affine bundles over M . We realize D branes on M as special submanifolds of these affine bundles. As an application of this geometric understanding of the B field, we give a simple geometric explanation for the ChernSimons modification of the field strength of the hetero...
متن کامل