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Curated by: DIBEOS (88 videos)
Introduction: (00:00-01:19) Chapter 1: Manifolds (00:01:19-00:10:35) https://dibeos.net/2025/04/12/how-to-get-to-manifolds-naturally/ Chapter 2: How to do Calculus on manifolds (00:10:35-00:19:04) https://dibeos.net/2025/04/12/how-to-do-calculus-on-an-abstract-manifold/ Chapter 3: What Differential Geometry is all about (00:19:04-00:32:16) https://dibeos.net/2025/04/12/the-core-of-differential-geometry/ Chapter 4: Tangent spaces in Differential Geometry (00:32:16-00:44:12) https://dibeos.net/2025/04/12/what-are-tangent-spaces-in-differential-geometry/ Chapter 5: Schwarzschild spacetime (00:44:12-00:54:00) https://dibeos.net/2025/04/06/the-mathematics-behind-the-schwarzschild-solution/ Chapter 6: What curvature really is (00:54:00-1:11:01) https://dibeos.net/2025/04/12/the-intuition-behind-curved-spaces/ Chapter 7: The mathematics of Minkowski spacetime (1:11:01-1:33:01) https://dibeos.net/2025/04/06/the-mathematics-of-minkowski-spacetime/ Chapter 8: Riemannian manifolds (1:33:01-1:46:57) https://dibeos.net/2025/05/03/riemannian-manifolds-in-12-minutes/ Chapter 9: Gaussian curvature (1:46:57-2:00:34) https://dibeos.net/2025/05/10/how-to-describe-a-surface-with-2-numbers/ Chapter 10: Ricci curvature tensor (2:00:34-2:10:11) https://dibeos.net/2025/05/17/how-to-describe-an-entire-space-with-a-matrix-ricci-curvature/ Chapter 11: Scalar curvature (2:10:11-2:22:34) https://dibeos.net/2025/05/24/how-a-single-real-number-determines-curvature/ Chapter 12: Conformal geometry (2:22:34-2:39:02) https://dibeos.net/2025/06/07/why-spacetime-isnt-always-curved/ Chapter 13: Metric tensor (2:39:02-2:50:11) https://dibeos.net/2025/06/21/how-would-you-measure-distances-in-curved-spaces/ Chapter 14: Tensor calculus (2:50:11-3:07:23) https://dibeos.net/2025/07/05/the-core-of-tensor-calculus/ Chapter 15: Intrinsic curvature (3:07:23-3:19:22) https://dibeos.net/2025/07/19/what-is-the-universe-expanding-into-according-to-pure-math/ Chapter 16: Differential forms (3:19:22-3:40:04) https://dibeos.net/2025/08/09/the-core-of-differential-forms/ Chapter 17: Geodesic equation (3:40:04-3:59:05) https://dibeos.net/2025/09/06/top-5-methods-for-solving-the-geodesic-equation/ Chapter 18: Tensor impostors (3:59:05-4:09:34) https://dibeos.net/2025/09/13/why-tensor-impostors-fool-so-many-people/ Chapter 19: The right side of Einstein’s equations (4:09:34-4:18:40) https://dibeos.net/2025/09/20/mathematician-vs-physicist-whats-on-the-right-side-of-einsteins-equation/ Chapter 20: The main solutions to Einstein’s field equations (4:18:40-4:32:57) https://dibeos.net/2025/10/29/the-main-solutions-of-einstein-field-equations/ Books: Catalogue of spacetimes: https://arxiv.org/pdf/0904.4184 General Relativity (Wald): https://amzn.to/4hAJymk Gravitation (Misner, Thorne, Wheeler): https://amzn.to/3WvPAuJ Spacetime and Geometry: An Introduction to General Relativity (Carroll): https://amzn.to/4ofaNVU Our website and email contact: https://dibeos.net/ dibeos.contact@gmail.com