Darboux-Lie derivatives
arXiv:2409.06596 · doi:10.1016/j.difgeo.2025.102305
Abstract
We introduce the Darboux-Lie derivative for fiber-bundle maps from natural bundles to associated fiber bundles and study its properties.
Final version, 25 pages. Compared with v1, there was a conceptual reorganization based on a more general concept called the "alpha-derivative". The Darboux-Lie derivative is defined as a specific application of this more general concept. We added examples that show how classical Lie derivatives and covariant derivatives can be seen as special cases of the new derivatives