Differential geometry

Related lectures (32)

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

Explores the definition of connections for smooth vector fields on manifolds.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

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

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