Stereographic Projection and Metric Tensors

Related lectures (28)

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

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Introduces the 5th postulate in Euclidean geometry and explores non-Euclidean geometries and their implications.

Explores non-Euclidean geometries, hyperbolic and spherical, challenging the traditional Euclidean geometry with implications for modern mathematics.