From the Fermi-Walker to the Cartan connection

Lafuente, Javier, and Salvador, Beatriz. "From the Fermi-Walker to the Cartan connection." Proceedings of the 19th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2000. 149-156. <http://eudml.org/doc/221070>.

@inProceedings{Lafuente2000,
abstract = {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 !},
author = {Lafuente, Javier, Salvador, Beatriz},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {149-156},
publisher = {Circolo Matematico di Palermo},
title = {From the Fermi-Walker to the Cartan connection},
url = {http://eudml.org/doc/221070},
year = {2000},
}

TY - CLSWK
AU - Lafuente, Javier
AU - Salvador, Beatriz
TI - From the Fermi-Walker to the Cartan connection
T2 - Proceedings of the 19th Winter School "Geometry and Physics"
PY - 2000
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 149
EP - 156
AB - 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 !
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221070
ER -