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Differential Geometry I
Last Updated: 2026-02-05 16:02:09
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.
Objective
Introduce the classical theory of curves and surfaces (which is the precursor of modern Riemannian geometry). Invite students to use and sharpen their geometric intuition. Introduce the language, basic tools, and some fundamental results in modern differential geometry.
Resources
Lecture Notes
Partial lecture notes are available from Prof. Lang's websitehttps://people.math.ethz.ch/~lang/
Literature
- Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces - John M. Lee: Introduction to Smooth Manifolds - S. Montiel, A. Ros: Curves and Surfaces - S. Kobayashi: Differential Geometry of Curves and Surfaces - Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten - Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 180 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Differential Geometry I |
|
4 h weekly |
| exercise |
Differential Geometry I
Groups are selected in myStudies.
Thu 13-14 or Thu 16-17 or Fri 13-14
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|
1 h weekly |
Offered In
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Physics Bachelor (no course offering in this semester)
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Bachelor Core Courses: Pure Mathematics (Further restrictions apply, but in particular: 401-3531-00L Differential Geometry I can only be recognised for the Master Programme if 401-3532-00L Differential Geometry II has not been recognised for the Bachelor Programme. Analogously for: 401-3461-00L Functional Analysis I - 401-3462-00L Functional Analysis II 401-3001-61L Algebraic Topology I - 401-3002-12L Algebraic Topology II 401-3132-00L Commutative Algebra - 401-3146-12L Algebraic Geometry For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
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