Responsibles: Christoph Stephan & Florian Hanisch

In the lecture Differential Geometry we learn the basic concepts of the geometry of curved spaces. We define the measurement of lengths and angles with the help of semi-riemannian metrics. We introduce a covariant derivative for vector fields and study locally shortest connections between two points, so-called geodesics. We then deal with various notions of curvature. This lecture is useful for students who want to understand the mathematical foundations of general relativity.

The course will be taught in German or in English.

Lecture and exercise programme:

All necessary information can be found here: Moodle

Semester (recommendation):
from 4th semester

Modul Numbers:
MAT-VM-D611, MAT-VM-D612, MATVMD814, MATVMD711, MAT-LS-WP1

Required prior knowledge:
Analysis 1+2 (3+4 favourable)

Literature:
1. C. Bär: Differential geometry, lecture notes, Potsdam 2013
2. C. Bär: Differentialgeometrie, Vorlesungsskript, Potsdam 2006
3. B. O'Neill: Semi-Riemannian Geometry, Academic Press, New York 2002