Exotic sphere

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Related lectures (29)

Covers second-order retractions in optimization on manifolds, focusing on smooth curves and their relation to the gradient and Hessian of a function.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Planes and Cylinders: Ray Intersections and Implementations

Covers the implementation of ray intersections with planes, cylinders, and spheres.

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Advanced Physics I

Covers empirical forces, applications of Newton's laws, momentum, and friction in physics.

Untitled

Riemannian metrics and gradients: Examples and Riemannian submanifolds

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

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.

Surface Integrals: Implicit Surfaces

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

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