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Geometria Diferencial de Curvas e Superfícies - Aula 22

Offered By: Instituto de Matemática Pura e Aplicada via YouTube

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Differential Geometry Courses Torsion Courses Curvature Courses Mean Curvature Courses Gauss Map Courses

Course Description

Overview

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Explore a comprehensive graduate-level lecture on Differential Geometry of Curves and Surfaces, delivered by Professor Lucas Ambrozio as part of the 2023 Summer School at the Instituto de Matemática Pura e Aplicada. Delve into advanced topics such as curves in plane and space, length, curvature, torsion, surfaces in R3, parameterizations, coordinate changes, tangent planes, fundamental forms, Gaussian curvature, mean curvature, Gauss normal map, principal curvatures, asymptotic lines, and intrinsic vs. extrinsic geometry. Examine key theorems including the sphere rigidity theorem, Alexandrov's theorem, Gauss's Theorema Egregium, and the Gauss-Bonnet theorem. Gain insights into covariant derivatives, parallel transport, geodesic curvature, and geodesics. Prerequisites include familiarity with the inverse function theorem in Rn and basic topology of Rn space.

Syllabus

(02/03/2023) - Mestrado: Geometria Diferencial de Curvas e Superfícies - Lucas Ambrozio - Aula 22


Taught by

Instituto de Matemática Pura e Aplicada

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