Understanding Parallel Transport & Connections in Differential Geometry

To master Riemannian Curvature, one must first grasp the concepts of Parallel Transport & Connections, mathematical tools which function as the essential bridges between flat spaces and curved ones. Discover how these simple concepts give us powerful insight into the nature of Differential Geometry, while advancing us towards our ultimate goal of rendering concrete the notion of curved spacetime. Plus, Jon Snow knows nothing -- except how to conduct Parallel Transport!

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Contents:
00:00 - Intro
00:45 - Parallel Transport
03:43 - The Riemannian Trick
04:53 - Parallel Transport on Curved Surfaces
07:25 - Infinitesimal Case
09:36 - Levi-Civita Connection
11:53 - Alternate Connections
13:46 - Conclusion