Distance and geodesics: Distance, geodesics and complete manifolds

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

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

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

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

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

Explores geodesics in the Wasserstein space, emphasizing constant speed geodesics and their properties.

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Explores the definition of connections for smooth vector fields on manifolds.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.