Submanifold

Related lectures (25)

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Explores smooth functions on manifolds, emphasizing continuity and atlas topologies.

Explores computing gradients on Riemannian manifolds through extensions and retractions, emphasizing orthogonal projectors and smooth extensions.

Explores smooth manifolds through defining functions and submanifolds, highlighting the importance of smoothness.

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the Grassmann manifold and retractions on submanifolds.

Discusses the challenges in differentiating vector fields on submanifolds and the importance of choosing the right method.

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

Explores tangent spaces as free movement directions on submanifolds, offering a geometrically satisfying linearization notion.