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 $CO\left(M\right)$ 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 $T_b\left(CO\left(M\right)\right)$. Finally, using the lift functions $k_b$, $b\in CO\left(M\right)$, the authors construct a trivialization of the fiber bundle $CO{\left(M\right)}_1$ over $CO\left(M\right)$, $CO{\left(M\right)}_1$, denoting the first prolongation of !

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

@article{701657,
     title = {From the Fermi-Walker to the Cartan connection},
     booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2000},
     pages = {149-156},
     mrnumber = {MR1758090},
     zbl = {1009.53019},
     url = {http://dml.mathdoc.fr/item/701657}
}

Lafuente, Javier; Salvador, Beatriz. From the Fermi-Walker to the Cartan connection, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books,  (2000), pp. 149-156. http://gdmltest.u-ga.fr/item/701657/