Tangent spaces and Riemannian manifolds

In this video, we give three alternative ways to view tangent vectors on manifolds. The first is dynamic, viewing tangent vectors as velocities of trajectories, the second is via identifying tangent vectors with their directional derivatives. Lastly, we consider the dual approach, defining first the cotangent space via differentials. We then give the definition of Riemannian manifolds and show how this concept allows one to define lengths of curves on a manifold.

Видео Tangent spaces and Riemannian manifolds канала DanielChanMaths