Linear Transports along Paths in Vector Bundles I. General Theory
نویسنده
چکیده
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 ones in a senses that there exist frames in which their matrices are unit. The investigated transports along paths are described in terms of their local coefficients, as well as in terms of derivations along paths.
منابع مشابه
Linear Transports along Paths in Vector Bundles II. Some Applications
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 algebras are investigated. A possible generalization of the theory of geodesics is proposed when the parallel transport generated by a linear connection is repla...
متن کاملTransports along Paths in Fibre Bundles III. Consistency with Bundle Morphisms
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 acting in it is considered. The consistency between linear transports along paths in a vector bundle and a Hermitian structure in it is studied.
متن کاملNormal frames and linear transports along paths in line bundles . Applications to classical electrodynamics
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 classical electrodynamics. The inertial frames for this theory are discussed. Bozhidar Z. Iliev: Normal frames and transports in line bundles. Electrodynamics 1
متن کاملLinear Transports along Paths in Vector Bundles IV. Consistency with Bundle Metrics
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 metrics (resp. transports) consistent with a given transport (resp. metric) are explicitly obtained. The special case of linear transports, generated by deriv...
متن کاملLinear Transports along Paths in Vector Bundles III. Curvature and Torsion
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.
متن کامل