The rolling tangent space, a forgotten vision on parallel transport and geodesics

Constant Pinteaux, Gijs M. Tuynman

Given a submanifold $M\subset {\mathbf{R}}^{\nu }$, a curve $\gamma :I\to M$ and tangent vectors $v$ along $\gamma$, we roll the tangent space along $\gamma$. In doing so, we get an imprint/trace of $\gamma$…