Geodesics and Parallel Transport

Related lectures (32)

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

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

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

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

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

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

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.