Manifolds and Tangent Space

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Related lectures (32)

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Manopt: Optimization Toolbox for Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Optimization on Manifolds

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

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

All things Riemannian: metrics, (sub)manifolds and gradients

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

Hands on with Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

General Manifolds and Topology

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

Grassmann manifold and Retractions

Covers the Grassmann manifold and retractions on submanifolds.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Conformal Symmetries in Euclidean and AdS Spaces

Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.