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
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 8: The Levi-Civita connection
Lecture 8: The Levi-Civita connection
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 9: Pseudo-Riemannian submanifolds
Lecture 9: Pseudo-Riemannian submanifolds
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 10: Normal coordinates (1)
Lecture 10: Normal coordinates (1)
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 11: Normal coordinates (2)
Lecture 11: Normal coordinates (2)
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 12: Densities on manifolds, Distance on a Riemannian manifold
Lecture 12: Densities on manifolds, Distance on a Riemannian manifold
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 13: Riemannian manifolds as metric spaces 1
Lecture 13: Riemannian manifolds as metric spaces 1
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 14: Riemannian manifolds as metric spaces (2)
Lecture 14: Riemannian manifolds as metric spaces (2)
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 15: Sectional, Ricci and scalar curvatures
Lecture 15: Sectional, Ricci and scalar curvatures
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 16: Ricci and scalar curvature and geodesic balls
Lecture 16: Ricci and scalar curvature and geodesic balls
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 17: Ricci curvature and fundamental group
Lecture 17: Ricci curvature and fundamental group
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 18: A primer on Lie groups
Lecture 18: A primer on Lie groups
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 19: Compact semisimple Lie groups are Einstein manifolds
Lecture 19: Compact semisimple Lie groups are Einstein manifolds
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 20: A primer on Kahler manifolds
Lecture 20: A primer on Kahler manifolds
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 21: Ricci form and Calabi-Yau theorem
Lecture 21: Ricci form and Calabi-Yau theorem
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 22: Calabi-Yau theorem, Quaternion Kahler manifolds
Lecture 22: Calabi-Yau theorem, Quaternion Kahler manifolds
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 23: Quaternion Kahler manifolds are Einstein
Lecture 23: Quaternion Kahler manifolds are Einstein
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 24: Further topics (1)
Lecture 24: Further topics (1)
![](https://www.google.com/images/icons/product/drive-32.png)
Lecture 25: Further topics (2)
Lecture 25: Further topics (2)
![](https://www.google.com/images/icons/product/drive-32.png)