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

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Lecture 8: The Levi-Civita connection

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Lecture 9: Pseudo-Riemannian submanifolds

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Lecture 10: Normal coordinates (1)

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Lecture 11: Normal coordinates (2)

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Lecture 12: Densities on manifolds, Distance on a Riemannian manifold

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Lecture 13: Riemannian manifolds as metric spaces 1

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Lecture 14: Riemannian manifolds as metric spaces (2)

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Lecture 15: Sectional, Ricci and scalar curvatures

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Lecture 16: Ricci and scalar curvature and geodesic balls

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Lecture 17: Ricci curvature and fundamental group

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Lecture 18: A primer on Lie groups

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Lecture 19: Compact semisimple Lie groups are Einstein manifolds

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Lecture 20: A primer on Kahler manifolds

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Lecture 21: Ricci form and Calabi-Yau theorem

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Lecture 22: Calabi-Yau theorem, Quaternion Kahler manifolds

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Lecture 23: Quaternion Kahler manifolds are Einstein

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Lecture 24: Further topics (1)

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Lecture 25: Further topics (2)

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