Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606143 | Differential Geometry and its Applications | 2013 | 26 Pages |
Abstract
To each second-order ordinary differential equation Ï on a smooth manifold M a G-structure PÏ on J1(R,M) is associated and the Chern connection âÏ attached to Ï is proved to be reducible to PÏ; in fact, PÏ coincides generically with the holonomy bundle of âÏ. The cases of unimodular and orthogonal holonomy are also dealt with. Two characterizations of the Chern connection are given: The first one in terms of the corresponding covariant derivative and the second one as the only principal connection on PÏ with prescribed torsion tensor field. The properties of the curvature tensor field of âÏ in relationship to the existence of special coordinate systems for Ï are studied. Moreover, all the odd-degree characteristic classes on PÏ are seen to be exact and the usual characteristic classes induced by âÏ determine the Chern classes of M. The maximal group of automorphisms of the projection p:RÃMâR with respect to which âÏ has a functorial behaviour, is proved to be the group of p-vertical automorphisms. The notion of a differential invariant under such a group is defined and stated that second-order differential invariants factor through the curvature mapping; a structure is thus established for KCC theory.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
J. Muñoz Masqué, M. Eugenia Rosado MarÃa,