Transporters: a proxy for parallel transport

This lecture discusses the concept of transporters as a practical alternative to parallel transport, highlighting the challenges and benefits. It covers the minimal requirements for moving vectors, examples with positive definite and rotation matrices, and the smooth dependence on x and y. The instructor explains the pragmatic choices involved in defining transporters and their use cases, emphasizing their role in optimization on manifolds. Additionally, the lecture explores algorithms like nonlinear CG and BFGS, finite differences, and the Hessf(x) function near critical points.