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