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Differential Geometry I
Last Updated: 2026-02-05 15:35:47
Abstract
This will be an introductory course in differential geometry.Topics covered include:- Smooth manifolds, submanifolds, vector fields,- Lie groups, homogeneous spaces,- Vector bundles, tensor fields, differential forms,- Integration on manifolds and the de Rham theorem,- Principal bundles.
Resources
Literature
There are many excellent textbooks on differential geometry. A friendly and readable book that covers everything in Differential Geometry I is: John M. Lee "Introduction to Smooth Manifolds" 2nd ed. (2012) Springer-Verlag. A more advanced (and far less friendly) series of books that covers everything in both Differential Geometry I and II is: S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volumes I and II (1963, 1969) Wiley.
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
"Hybrid"
Starting in October, a mixed form of online and classroom teaching will be offered.
As of November, online for all students.
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4 h weekly |
| exercise |
Differential Geometry I
Groups are selected in myStudies.
Thu 13-14 or Thu 14-15 or Thu 16-17 or Fri 13-14
|
|
1 h weekly |
Offered In
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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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