Pseudo-Riemannian manifold

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

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Explores linear convergence with the Polyak-Łojasiewicz condition on a Riemannian manifold.

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

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

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

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

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.