Differential Geometry of Curves and Surfaces — 1^{st} Semester — 2023/2024
AnnoucementsHomework 9 is due on November 30. SyllabusCurves: curves, curvature, torsion, Frenet-Serret formulas, global theorems. Differentiable manifolds: differentiable manifolds in R^{n}, tangent space, normal space, parameterizations. Differential forms: covectors in R^{n}, exterior product, differential forms, pull-back, exterior derivative, integration, Stokes Theorem. Surfaces: first and second fundamental forms, mean curvature, Gauss curvature. Geometry of surfaces: connection and curvature forms, structure equations, Theorema Egregium of Gauss, vector fields, covariant derivative, parallel transport, geodesics. Gauss-Bonnet Theorem: triangulations, Euler's characteristic, Gauss-Bonnet Theorem. Minimal surfaces: examples, isothermal coordinates, Weierstrass-Enneper representation. BiliographyMain
Secundary
Grading PolicyHomework: Makes up 50% of the grade. Late homework will not be accepted. Final exam: Makes up 50% of the grade. Can be retaken if necessary. Additional ResourcesDifferentiable manifolds and differential forms Homework
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