Differential Geometry

Module MA3205

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA3205 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Content, Learning Outcome and Preconditions


Smooth Manifolds, tangential, vector, and principal bundles, Riemannian metrics, curvature tensor, geodesics, symmetric spaces, Liegroups.

Learning Outcome

After successful completion of this course, the students know how metric properties of the euclidean space are extended to "curved" spaces. They are able to apply this curvature theory to derive properties of these spaces using analytic methods.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, MA2204 Elementary Differential Geometry

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Differential Geometry Hoffmann, T. Dienstag, 10:15–11:45
Donnerstag, 16:00–18:00

Learning and Teaching Methods

lecture, exercise course, self-study assignments


blackboard or computer


do Carmo: Riemannian Geometry, Birkhäuser, 1992. Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces, AMS 2001. Kühnel: Differential Geometry: Curves - Surfaces - Manifolds, AMS, 2005.

Module Exam

Description of exams and course work


Exam Repetition

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.