Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-09-30
JP J.Geom.Topol. 5 (2005) 187-250
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
In this version, the paper is restructured and revised. The appendix is removed and the references are updeated. The packages
Scientific paper
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 matrix or their coefficients vanish. A number of results, including theorems of existence and uniqueness, concerning normal frames are derived. Special attention is paid to the important case when the bundle's base is a manifold. The normal frames are defined and investigated also for derivations along paths and along tangent vector fields in the last case. It is proved that normal frames always exist at a single point or along a given (smooth) path. On other subsets normal frames exist only as an exception if (and only if) certain additional conditions, derived here, are satisfied. Gravity physics and gauge theories are pointed out as possible fields for application of the results obtained.
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