401-3531-00L Differential Geometry I
| Semester | Herbstsemester 2024 |
| Dozierende | U. Lang |
| Periodizität | jährlich wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
| Kommentar | Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar. Die Kategoriezuordnung können Sie in diesem Fall nicht selber in myStudies vornehmen, sondern Sie müssen sich dazu nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (www.math.ethz.ch/studiensekretariat) wenden. |
| Kurzbeschreibung | Introduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in R^n, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem. | |||||||||||||||||||||
| Lernziel | Learn the basic concepts and results in differential geometry and differential topology. Learn to describe, compute, and solve problems in the language of differential geometry. | |||||||||||||||||||||
| Inhalt | Curves, (hyper-)surfaces in R^n, first and second fundamental forms, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet, minimal surfaces. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem. | |||||||||||||||||||||
| Skript | Partial lecture notes are available from https://people.math.ethz.ch/~lang/ | |||||||||||||||||||||
| Literatur | Differential geometry in R^n: - Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces - S. Montiel, A. Ros: Curves and Surfaces - Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten - Christian Bär: Elementare Differentialgeometrie Differential topology: - Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds - Victor Guillemin & Alan Pollack: Differential Topology - Morris W. Hirsch: Differential Topology - John M. Lee: Introduction to Smooth Manifolds | |||||||||||||||||||||
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