Riemannian manifold

Related lectures (32)

Page 3 of 4

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Explores distance, geodesics, and complete manifolds, emphasizing the existence of minimizing geodesics and the concept of metric completeness.

Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores computing gradients on Riemannian manifolds through extensions and retractions, emphasizing orthogonal projectors and smooth extensions.

Introduces trust region methods and presents an example of Max-Cut Burer-Monteiro rank 2 optimization.

Introduces geodesic convexity on Riemannian manifolds and explores its properties.