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German original

Differential Geometry II
(dt. Differentialgeometrie II)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
Regelmäßig im Wechsel mit anderen advanced moduleen im Gebiet Analysis/Geometrie
Person in charge of the module's outline Prof. Dr. Ilka Agricola

Contents

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

The students should deepen their geometric knowledge and get to know physical applications, learn modern techniques for scientific work in this field, practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, demonstration), improve their oral communication skills in the exercises by practicing free speech in front of an audience and during the discussion.


Prerequisites

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.


Recommended Reading

  • 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. Michael 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 Wintersemester 2019/20. 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.