Einstein manifolds
The textbook is Einstein Manifolds, by A. L. Besse
Lecture 1: Overview of the course
Lecture 1: Overview of the course
Lecture 2: Linear connections on vector bundles I
Lecture 2: Linear connections on vector bundles I
Lecture 3: Linear connections on vector bundles II, Curvature, Torsion
Lecture 3: Linear connections on vector bundles II, Curvature, Torsion
Lecture 4: Torsion, Bianchi identity, Parallel transport
Lecture 4: Torsion, Bianchi identity, Parallel transport
Lecture 5: Geodesics of a connection, Exponential map
Lecture 5: Geodesics of a connection, Exponential map
Lecture 6: Jacobi fields of a connection
Lecture 6: Jacobi fields of a connection
Lecture 7: Riemannian and pseudo-Riemannian manifolds
Lecture 7: Riemannian and pseudo-Riemannian manifolds
zoom_0.mp4
Lecture 8: The Levi-Civita connection
Lecture 8: The Levi-Civita connection
zoom_Sept29.mp4
Lecture 9: Pseudo-Riemannian submanifolds
Lecture 9: Pseudo-Riemannian submanifolds
zoom_Oct1.mp4
Lecture 10: Normal coordinates (1)
Lecture 10: Normal coordinates (1)
zoom_0Oct6.mp4
Lecture 11: Normal coordinates (2)
Lecture 11: Normal coordinates (2)
zoom_Oct8.mp4
Lecture 12: Densities on manifolds, Distance on a Riemannian manifold
Lecture 12: Densities on manifolds, Distance on a Riemannian manifold
zoom_Oct13.mp4
Lecture 13: Riemannian manifolds as metric spaces 1
Lecture 13: Riemannian manifolds as metric spaces 1
zoom_Oct15.mp4
Lecture 14: Riemannian manifolds as metric spaces (2)
Lecture 14: Riemannian manifolds as metric spaces (2)
zoom_Oct20.mp4
Lecture 15: Sectional, Ricci and scalar curvatures
Lecture 15: Sectional, Ricci and scalar curvatures
zoom_Oct22.mp4
Lecture 16: Ricci and scalar curvature and geodesic balls
Lecture 16: Ricci and scalar curvature and geodesic balls
zoom_Oct27.mp4
Lecture 17: Ricci curvature and fundamental group
Lecture 17: Ricci curvature and fundamental group
zoom_Oct29.mp4
Lecture 18: A primer on Lie groups
Lecture 18: A primer on Lie groups
zoom_Nov3.mp4
Lecture 19: Compact semisimple Lie groups are Einstein manifolds
Lecture 19: Compact semisimple Lie groups are Einstein manifolds
zoom_November5.mp4
Lecture 20: A primer on Kahler manifolds
Lecture 20: A primer on Kahler manifolds
zoom_November10.mp4
Lecture 21: Ricci form and Calabi-Yau theorem
Lecture 21: Ricci form and Calabi-Yau theorem
zoom_Nov12.mp4
Lecture 22: Calabi-Yau theorem, Quaternion Kahler manifolds
Lecture 22: Calabi-Yau theorem, Quaternion Kahler manifolds
zoom_Nov17.mp4
Lecture 23: Quaternion Kahler manifolds are Einstein
Lecture 23: Quaternion Kahler manifolds are Einstein
zoom_Nov19.mp4
Lecture 24: Further topics (1)
Lecture 24: Further topics (1)
zoom_december1.mp4
Lecture 25: Further topics (2)
Lecture 25: Further topics (2)
zoom_december3.mp4