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Title: From the Fermi-Walker to the Cartan connection (English)
Author: Lafuente, Javier
Author: Salvador, Beatriz
Language: English
Journal: Proceedings of the 19th Winter School "Geometry and Physics"
Issue: 1999
Pages: 149-156
Category: math
Summary: 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 ! (English)
MSC: 53C05
MSC: 53C10
MSC: 53C20
idZBL: Zbl 1009.53019
idMR: MR1758090
Date available: 2009-07-13T21:43:54Z
Last updated: 2012-09-18
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