The Christoffel Symbols In Riemannian Geometry скачать в хорошем качестве

The Christoffel Symbols In Riemannian Geometry

The illustrious Christoffel Symbols are requisite to any study of curved surfaces, but can their abstract nature be made more concrete and physical? Here our exploration of the daunting subject of differential geometry continues, as with a host of vivid and visceral 3D animations we attempt to explore the nature of these mathematical objects, whilst striving to bring the wonderful world of Riemannian Geometry to life! We highly recommend watching "An Introduction to Curvilinear Coordinates" before viewing this video:    • An Introduction to Curvilinear Coordinates...   If you're completely new to the subject of the Christoffel Symbols, try starting here:    • Conceptualizing the Christoffel Symbols: A...   Lastly, a huge thank you to our Patreon supporters, for continuing to make our channel a feasible endeavor. Especial thanks to the following individuals: Henry Lindner Antsu Sausanen Michael O'Connor James Bretz Jordan Rosario Please consider supporting the channel here:   / dialect_philosophy   Video Contents: 00:00 - Introduction 00:50 - Curvilinear Coordinate Recap 02:17 - Basis Vectors & Christoffel Symbols: Physical Intuition 06:49 - Basis Vectors & Christoffel Symbols on a Curved Manifold 13:17 - Extrinsic Solution of a 2-Sphere 14:49 - Metric Tensor & Intrinsic Method 19:15 - Levi-Civita Constraints; Christoffel Equation Derivation & Interpretation 27:04 - Example Problem/Intrinsic Solution of a 2-Sphere 31:20 - Global vs. Local Flatness/Conclusion