L-regular linear connections
| dc.creator | Youssef, Nabil L. | |
| dc.creator | Tamim, Aly A. | |
| dc.date | 2006-08-13 | |
| dc.date | 2006-08-16 | |
| dc.date.accessioned | 2026-07-07T07:21:42Z | |
| dc.date.available | 2026-07-07T07:21:42Z | |
| dc.description | The aim of this paper is to generalize the theory of nonlinear connections of Grifone ([3] and [4]). We adopt the point of view of Anona [1] and continue developing the approach established by the first author in [10]. The first part of the work is devoted to the problem of associating to each $L$-regular linear connection on $M$ a nonlinear $L$-connection on $M$. The route we have followed is significantly different from that of Grifone. We introduce an almost-complex and an almost-product structures on $M$ by means of a given $L$-regular linear connection on $M$. The product of these two structures defines a nonlinear $L$-connection on $M$, which generalizes Grifone's nonlinear connection. The seconed part is devoted to the converse problem: associating to each nonlinear $L$-connection \G on $M$ an $L$-regular linear connection on $M$; called the $L$-lift of \G. The existence of this lift is established and the fundamental tensors associated with it are studied. In the third part, we investigate the $L$-lift of a homogeneous $L$-connection \G, called the Berwald $L$-lift of \G. Then we particularize our study to the $L$-lift of a conservative $L$-connection. This $L$-lift enjoys some interesting properties. We finally deduce various identities concerning the curvature tensors of such a lift. Grifone's theory can be retrieved by letting $M$ be the tangent bundle of a differentiable manifold and $L$ be the natural almost-tangent structure $J$ on $M$. | |
| dc.description | 12 pages, LaTeX file, Minor change (concerning reference No. 10) | |
| dc.identifier | https://arxiv.org/abs/math/0608314 | |
| dc.identifier | http://arxiv.org/abs/math/0608314 | |
| dc.identifier | Tensor, N. S., Vol. 60 (1998), 144-154 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115396 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C15, 53C05 | |
| dc.title | L-regular linear connections | |
| dc.type | text |