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From the Fermi-Walker to the Cartan connection

Lafuente, Javier; Salvador, Beatriz — 2000

Proceedings of the 19th Winter School "Geometry and Physics"

Let $M$ be a $C^{\infty}$ -manifold with a Riemannian conformal structure $C$ . Given a regular curve $γ$ on $M$ , the authors define a linear operator on the space of (differentiable) vector fields along $γ$ , only depending on $C$ , called the Fermi-Walker connection along $γ$ . Then, the authors introduce the concept of Fermi-Walker parallel vector field along $γ$ , proving that such vector fields set up a linear space isomorphic to the tangent space at a point of $γ$ . This allows to consider the Fermi-Walker horizontal lift of...

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