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Differential Geometry II
Last Updated: 2026-02-05 16:22:40
Abstract
This is a continuation course of Differential Geometry I. Topics covered include:Introduction to Riemannian geometry: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, and isoperimetric inequalities.
Objective
Providing an introductory invitation to Riemannian geometry.
Resources
Literature
- M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - I. Chavel, "Riemannian Geometry: A Modern Introduction" 2nd ed. (2006), CUP, - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004 - S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I (1963) Wiley,
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Differential Geometry II |
|
4 h weekly |
| exercise |
Differential Geometry II
Groups are selected in myStudies.
Fri 9-10 or Fri 10-11
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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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