Hessians, Symmetry and Examples: Sphere, Stiefel

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

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

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

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

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

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

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Explores comparing tangent vectors and parallel transport on manifolds.

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