Pseudo-Riemannian manifold

Related lectures (30)

Page 3 of 3

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Explores geodesic convexity, focusing on properties of convex functions on manifolds.

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.

Explores gradient descent methods for optimizing functions on manifolds, emphasizing small gradient guarantees and global convergence.

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Explores matrix-based approaches for computing the Newton step on a Riemannian manifold.