Differential geometry

Related lectures (32)

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

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

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

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

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

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

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

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