Riemannian geometry

Related lectures (32)

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Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

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

Introduces the Riemannian Trust Regions (RTR) framework, covering conjugate directions, Newton's method, and model improvement.

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

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

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

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

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

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.