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Differential Geometry II
(dt. Differentialgeometrie II)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
One semester,
Regularly alternating with other specialization modules im Gebiet Analysis/Geometrie
Person in charge of the module's outline Prof. Dr. Ilka Agricola, Prof. Dr. Oliver Goertsches


At least one of the following topics:

  • Differential geometry of Lie groups as well as symmetric and homogeneous spaces
  • Symplectic geometry and theoretical mechanics
  • Principa fiber bundles and gauge field theory
  • General relativity theory and pseudo-Riemann's manifolds
  • Spin geometry and elliptic differential operators on manifolds

Qualification Goals


  • have deepened their knowledge of geometry
  • know physical applications of differential geometry
  • have learned modern techniques for scientific work in this field
  • have deepened mathematical working methods (developing mathematical intuition and its formal justification, abstraction skills, proofs),
  • have improved their oral communication skills in the exercises by practicing free speech in front of an audience and in discussion.


None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Algebra, Complex Analysis and Vector Analysis. In addition, basic knowledge of differential geometry is recommended.


Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying M.Sc. Computer Science, this module can be attended in the study area Profile Area Mathematics.

Recommended Reading

  • M. Audin, Torus actions on symplectic manifolds, Birkhäuser.
  • Th. Friedrich, Dirac-Operatoren in der Riemannschen Geometrie, Vieweg.
  • S. Helgason, Differential geometry, Lie groups, and symmetric spaces, AMS.
  • S. Kobayashi, K. Nomizu, Foundations of Differential Geometry 1 & 2, Wiley Classics Library.
  • M. Spivak, A comprehensive introduction to differential geometry, Berkeley, California: Publish Perish, Inc.

Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.