Year: 2024
Type: preprint
Abstract: This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It then implies easily the existence of global solutions to linear non-autonomous ODE's, with a standard time-dependent flow construction. As a further application, a simple proof of the smooth triviality of vector bundles over contractible bases is given. Finally, a detailed elementary proof of the isomorphy (as Lie algebras) of all fibers of the kernel of a transitive Lie algebroid is given.
Source: arXiv (Cornell University)
Author: Jotz, M.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403799221