Riemannian connections: What they are and why we care

Related lectures (32)

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

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

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

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

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

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

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

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

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.