Differential geometry of surfaces

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Differential geometry

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Related lectures (31)

Developable Surfaces and Parametrization

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

Surface Integrals: Implicit Surfaces

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

Analytic Manifolds and Berkovich Spaces

Introduces analytic manifolds, Berkovich spaces, and multiplicative semi-norms in K-algebras.

Heat Transfer from Extended Surfaces: Fins

Explores heat transfer from fins, discussing temperature profiles and performance of fin-based systems.

Differential Geometry: Parametric Curves & Surfaces

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

Differential Forms Integration

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

Mechanics of Kirchhoff Rods II

Explores the mechanics of Kirchhoff rods, focusing on 3D kinematics and twisted solutions.

Shells I

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

Fourier Analysis: Stokes Theorem

Explores the application of Stokes' theorem to surfaces and vector spaces in Fourier analysis.

3-dimensional Anosov flows: U(1)-extension and Exponential Mixing

Explores the U(1)-extension of Anosov diffeomorphisms and the proof of exponential mixing through uniform contractivity and cancellation by complex phases.

Ruled Surfaces: Generators and Applications

Explores ruled surfaces, surfaces generated by moving lines in space, including cones, cylinders, and hyperboloids, with applications in architecture.

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