Smooth maps on manifolds and differentials

Related lectures (32)

Page 1 of 4

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

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

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

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

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

Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.

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

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