Advanced Search

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...