VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.
Differential Geometry II
Last Updated: 2026-02-05 16:37:52
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.
Objective
Continuing the introduction to Riemannian geometry, with a focus on the role of curvature and the interplay of geometry and topology; and introducing fundamental aspects of Lorentzian geometry.
Resources
Literature
- M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I, Wiley 1963 - B. O'Neill, Semi-Riemannian Geometry With Applications to Relativity, Academic Press 1983
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 10-11 or Fri 11-12
|
|
1 h weekly |
Offered In
-
-
-
-
-
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.)
-
-
-
-
-