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Related lectures (31)

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Explores integral curves on manifolds and the significance of the exponential map in Lie groups.

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Covers smooth sets and functions on manifolds, with a focus on constructing an atlas for a circle.

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

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

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

Explains Riemannian submanifolds, metrics, and gradients computation on manifolds.

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

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

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.