Year: 2010
Type: article
Abstract: A manifold with an arbitrary affine connection is considered and the geodesic spray associated with the connection is studied in the presence of a Lie group action.In particular, results are obtained that provide insight into the structure of the reduced dynamics associated with the given invariant affine connection.The geometry of the frame bundle of the given manifold is used to provide an intrinsic description of the geodesic spray.A fundamental relationship between the geodesic spray, the tangent lift and the vertical lift of the symmetric product is obtained, which provides a key to understanding reduction in this formulation.
Author: Ajit Bhand
Institution: University of Oklahoma
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2147240326