From the Fermi-Walker to the Cartan connection

Lafuente, Javier ; Salvador, Beatriz

Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books, (2000), p. 149-156 / Harvested from

Résumé

Let $M$ be a $C^\infty $-manifold with a Riemannian conformal structure $C$. Given a regular curve $\gamma $ on $M$, the authors define a linear operator on the space of (differentiable) vector fields along $\gamma $, only depending on $C$, called the Fermi-Walker connection along $\gamma $. Then, the authors introduce the concept of Fermi-Walker parallel vector field along $\gamma $, proving that such vector fields set up a linear space isomorphic to the tangent space at a point of $\gamma $. This allows to consider the Fermi-Walker horizontal lift of $\gamma $ to the bundle $CO(M)$ of conformal frames on $M$ and to define, for any conformal frame $b$ at a point $p$, a lift function $k_b$ from the set of 2-jets of regular curves on $M$ starting at $p$ into the tangent space $T_b(CO(M))$. Finally, using the lift functions $k_b$, $b\in CO(M) $, the authors construct a trivialization of the fiber bundle $CO(M)_1$ over $CO(M)$, $CO(M)_1$, denoting the first prolongation of !

Détail

MR MR1758090 | Zbl 1009.53019

EUDML-ID : urn:eudml:doc:221070
Mots clés: