Metric connection

Related lectures (31)

Page 2 of 4

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

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

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Covers the definition and computation of Riemannian Hessians on manifolds.

Covers the advanced design of concrete structures focusing on the connections between elements.

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Explores parallel transport along loops and covariant derivatives induced by metrics.

Delves into phase transitions in random graphs, emphasizing the emergence of a giant component with varying connectivity.

Covers optimization on manifolds, smoothness, tools needed for optimization, and advanced algorithms using Hessians and Riemannian connections.