Rolling manifolds: an approach through geometric control

In this thesis, we present the problem of a manifold rolling on another using an intrinsic approach guided by control theory. We begin with an introductory example of a 2-dimensional sphere rolling on a plane and then extend the theory to a general 2-dimensional case. In this context, it is already possible to see that controllability translates into conditions on the Riemann tensors. In the second part, we study the problem in a general n-dimensional setting, presenting the complete theoretical framework.