Darboux-Lie derivatives
Differential Geometry
2025-10-20 v3
Abstract
We introduce the Darboux-Lie derivative for fiber-bundle maps from natural bundles to associated fiber bundles and study its properties.
Cite
@article{arxiv.2409.06596,
title = {Darboux-Lie derivatives},
author = {Antonio De Nicola and Ivan Yudin},
journal= {arXiv preprint arXiv:2409.06596},
year = {2025}
}
Comments
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