|
Title
|
|
|
|
The Berwald-type connection associated to time-dependent second-order differential equations
| |
|
Author
|
|
|
|
| |
|
Abstract
|
|
|
|
| We investigate the notions of a connection of Finsler type and of Berwald type on the first jet bundle J(1)pi of a manifold E which is fibred over IR. Such connections are associated to a given horizontal distribution on the bundle pi(1)(0) : J(1)pi --> E, which in particular may come from a time-dependent system of second-order ordinary differential equations. In order to accomodate three existing constructions of a Berwald-type connection for a second-order system, we first introduce equivalence classes of connections of Finsler and Berwald type. By exploring the differences between the existing models in more depth, we come to a new construction which in many respects can be regarded as giving an optimal representative of the class of Berwald-type connections. We briefly enter into two related matters: one is the definition of connections of the type of Cartan, Chern-Rund and Hashiguchi when a metric tensor field is given; the other one is the potential effect of the newly acquired insights on the theory of derivations on forms along the projection pi(1)(0). |
| |
|
Language
|
|
|
|
English
| |
|
Source (journal)
|
|
|
|
Houston journal of mathematics. - Houston, Tex.
| |
|
Publication
|
|
|
|
Houston, Tex.
:
2001
| |
|
ISSN
|
|
|
|
0362-1588
| |
|
Volume/pages
|
|
|
|
27
:4
(2001)
, p. 763-797
| |
|
ISI
|
|
|
|
000173864300006
| |
|