%0 Journal Article
%A Lafuente López, Javier
%A Salvador, Beatriz
%T From the Fermi-Walker to the Cartan connection
%D 2000
%@ 0009-725X
%U https://hdl.handle.net/20.500.14352/58340
%X Let M be a differentiable manifold and C ={e2org / a : M -> R } a Riemannian conformal structure on M. Given any regular curve in M, 7 : I -> M, there is a natural way of defining an operator, D/dt: £(7) -> £(7), the Fermi-Walkerconnection along 7, which only depends on the conformal structure C, and such that it coincides with the Fermi-Walker connection along 7 -in the classical sense- of anyg € C such that g("y'(t),y'(t)) = 1 Vt G I. This Fermi- Walker connection enables us to construct a lift-function Kb : T*M -> TbCO(M) for every b G CO(M), and p = n(b), n : CO(M) —> M being the usual projection. In some sense, Kb combines all the different lift-functions TPM -> T6CO(M) given by the Levi-Civita connections of the compatibles metrics g € C. But over all, Kb determines the conformal structure C over M, so that it may be used to know about the normal Cartan connection and the Weyl conformal curvature tensor.
%~