401-3531-00L Differential Geometry I
| Semester | Autumn Semester 2019 |
| Lecturers | U. Lang |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| Comment | At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. |
Courses
| Number | Title | Hours | Lecturers | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-3531-00 V | Differential Geometry I | 4 hrs |
| U. Lang | |||||||||
| 401-3531-00 U | Differential Geometry I Groups are selected in myStudies. Thu 14-15 or Thu 15-16 or Fri 13-14 | 1 hrs |
| U. Lang |
Catalogue data
| Abstract | 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. |
| Learning objective | |
| Lecture notes | Partial lecture notes are available from https://people.math.ethz.ch/~lang/ |
| Literature | Differential geometry in R^n: - Manfredo P. do Carmo: Differential Geometry of 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 |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 10 credits |
| Examiners | U. Lang |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 180 minutes |
| Written aids | None |
| This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| Main link | Information |
| Only public learning materials are listed. | |
Groups
| 401-3531-00 U | Differential Geometry I | ||||||
| Groups | G-01 |
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| G-02 |
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| G-03 |
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Restrictions
| There are no additional restrictions for the registration. |
