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This entry is from Summer semester 2018 and might be obsolete. You can find a current equivalent here.

Differential Geometry II
(dt. Differentialgeometrie II)

Level, degree of commitment Specialization 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(s): Written or oral examination
Examination type: Successful completion of at least 50 percent of the points from the weekly exercises.
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und in den Aufbaumodulen Algebra sowie Funktionentheorie und Vektoranalysis vermittelt werden, sowie Grundkenntnisse der Differentialgeometrie.


Applicability

The module 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. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

The module can also be used in other study programs (export module).

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Reinen Mathematics zugeordnet ist.


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 Summer semester 2018. 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.