Normal frames for general connections on differentiable fibre bundles
Abstract
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 existence of bundle coordinates normal at a given point and/or along injective horizontal path is proved. A necessary and sufficient condition of existence of bundle coordinates normal along injective horizontal mappings is derived.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- May 2006
- DOI:
- 10.1016/j.geomphys.2005.04.018
- arXiv:
- arXiv:math/0405004
- Bibcode:
- 2006JGP....56..780I
- Keywords:
-
- 02.40.Ma;
- 02.40.Vh;
- 02.40-k;
- 04.20.Cv;
- Global differential geometry;
- Global analysis and analysis on manifolds;
- Fundamental problems and general formalism;
- Mathematics - Differential Geometry;
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- General Relativity and Quantum Cosmology;
- 57R25 (Primary) 53B05;
- 53C05;
- 55R99;
- 58A30 (Secondary)
- E-Print:
- 24 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. In version 2 some results are generalized and proved under weaker conditions. For other papers on the same topic view the "publication" pages at http://theo.inrne.bas.bg/~bozho/