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Geometria Diferencial de Curvas e Superfícies - Aula 13

Offered By: Instituto de Matemática Pura e Aplicada via YouTube

Tags

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

Course Description

Overview

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Explore a comprehensive lecture on Differential Geometry of Curves and Surfaces in this 13th session of the Summer School 2023 master's course, delivered by Professor Lucas Ambrozio. Delve into advanced topics such as curves in planes and space, length, curvature, and torsion. Examine surfaces in R3, including parameterizations, coordinate changes, and tangent planes. Study the first fundamental form, distances, areas, and curvature concepts like Gaussian and mean curvature. Investigate the Gauss normal map, second fundamental form, principal curvatures, curvature lines, and asymptotic lines. Analyze intrinsic versus extrinsic geometry, isometries, and Gauss's Theorema Egregium. Explore covariant derivatives, parallel transport, geodesic curvature, and geodesics. Discover the Gauss-Bonnet Theorem and its applications, along with other global theorems and related topics. Prerequisite knowledge includes familiarity with the inverse function theorem in Rn and basic topology of Rn space.

Syllabus

(02/02/2023) - Mestrado: Geometria Diferencial de Curvas e Superfícies - Lucas Ambrozio - Aula 13


Taught by

Instituto de Matemática Pura e Aplicada

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