Lecture
Retractions, vector fields and tangent bundles: Retractions and vector fields
In course
DEMO: culpa duis
Aute commodo eiusmod veniam eiusmod veniam ad in. Fugiat commodo dolor duis do quis proident consectetur voluptate elit id ex Lorem officia ex. Tempor minim labore anim incididunt voluptate anim minim aliquip officia ad laborum aliquip. Nisi sit in duis ipsum occaecat do non ipsum mollit magna proident qui tempor ut. Amet ut sint enim cupidatat laborum aliqua velit cillum. Mollit laborum elit nisi voluptate proident est duis aliqua consectetur occaecat. Laboris sunt do non pariatur irure in id consectetur in laboris anim occaecat enim incididunt.
Description
This lecture covers the concept of retractions as smooth maps from the tangent bundle to the manifold, providing examples on Euclidean and spherical manifolds. It also introduces vector fields on manifolds, defining them as maps that assign a tangent vector to each point on the manifold, and discussing their smoothness and extension properties.
In MOOC
Introduction to optimization on smooth manifolds: first order methods
Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
Instructor
et incididunt ex
Aute quis commodo reprehenderit magna incididunt fugiat esse sint quis do. Quis veniam qui mollit nisi Lorem proident ex cupidatat mollit voluptate nisi. Cupidatat non pariatur cupidatat commodo mollit nisi occaecat nostrud labore nostrud occaecat commodo. Anim consectetur laborum ut Lorem voluptate deserunt adipisicing eu aliqua. Mollit aute et magna nostrud consectetur commodo pariatur commodo.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (46)
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Retractions vector fields and tangent bundles: Tangent bundlesMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.
Dynamics of Steady Euler Flows: New Results
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Connections: motivation and definition
Explores the definition of connections for smooth vector fields on manifolds.
Tangent Bundles and Vector Fields
Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.