Differential Geometry

What it is about

You learn the basics of smooth manifolds, bundles (tangent, vector, and principal bundles) as well as Riemannian metrics, curvature tensors and geodesics. In addition, symmetric spaces and Lie groups are treated. In the end you can transfer metric properties of Euclidean space to 'curved' spaces and derive properties of such spaces using analytical methods.

What you will be able to do

Understanding of smooth manifolds and associated bundles
Knowledge of Riemannian metrics and the curvature tensor
Computation and interpretation of geodesics
Application of curvature theory to geometric properties
Familiarity with symmetric spaces and Lie groups

What the module consists of

VorlesungPresentation of content, examples and discussion
Übung/Practice sessionsDeepening the content through problem sheets and solutions

Teaching method

LectureLecture with demonstrative examples and discussion to introduce topics
Exercise courseWorking on problems to deepen understanding and self-check
Self-study assignmentsIndependent study of the literature and analysis of the content

Dates

LectureDifferential Geometry [MA3205]2 groups to choose from

ATue10:15–11:45
00.07.014, Übungsraum (5607.EG.014)
14× · 13.10.–02.02.
- 13.10.
- 20.10.
- 27.10.
- 03.11.
- 17.11.
- 24.11.
- 01.12.
- 08.12.
- 15.12.
- 22.12.
- 12.01.
- 19.01.
- 26.01.
- 02.02.
BThu10:15–11:45
00.07.014, Übungsraum (5607.EG.014)
14× · 15.10.–04.02.
- 15.10.
- 22.10.
- 29.10.
- 05.11.
- 12.11.
- 19.11.
- 26.11.
- 10.12.
- 17.12.
- 07.01.
- 14.01.
- 21.01.
- 28.01.
- 04.02.

From the current semester, not binding. You attend one of several groups; the timetable automatically suggests the one with the fewest clashes.

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