Lecture
This lecture covers the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds. It explains the concept of parallel vector fields along curves and the covariant derivative induced by a connection. The lecture also discusses the properties of the operator that satisfies linearity, chain rule, and Leibniz rule. Additionally, it explores the parallel transport of vectors along curves and the linear map from time t₁ to t₂. The uniqueness of the parallel field along the curve is emphasized.