Submanifold

Related lectures (25)

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

Explores smooth maps between submanifolds, discussing smoothness criteria and composition preservation.

Explores how submanifolds can be deformed into linear patches using diffeomorphisms and the inverse function theorem.

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores fixed-rank matrices as an embedded submanifold, focusing on constructing local defining functions and efficiently computing tangent vectors.

Covers embedded submanifolds, Stiefel manifold, tangent spaces, and differential ranks.

Introduces smooth manifolds, emphasizing the importance of submanifolds of linear spaces.

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.