Differentiating Vector Fields: Definition

Related lectures (32)

Page 3 of 4

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

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

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

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

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

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

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