2014/12/21 by Fernand Pelletier, Pelletier, F.
Physics and Astronomy · #17B66 #53C05 #93B05 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1412.6742
openalex publication_date 2014/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pre-Lie algebroid is an anchored bundle provided with an almost Lie bracket such that the anchor is compatible with the Lie bracket of vector fields. We firstly show how most geometrical structures intensively studied in the framework of Lie algebroid can easily be extended in the pre-Lie algebroid context. The principal purpose of this paper is to show that how all these results only depend of the foliated structure and do not depend of the pre-Lie algebroid structure that we can put on a foliated anchored bundle. As application, we obtain a Finsler connection on a foliated anchored bundle which induces the classical Finsler connection on each leaf and a similar result for the Chern connection.