Riemannian connections

Related lectures (32)

Page 3 of 4

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.

Covers the concept of local frames, their construction, and limitations.

Discusses gradients on Riemannian submanifolds and the construction of local frames.

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

Covers optimization on manifolds, smoothness, tools needed for optimization, and advanced algorithms using Hessians and Riemannian connections.

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Covers the definition and computation of Riemannian Hessians on manifolds.