# Differential Geometry II

A selection of the following topics:

● Exponential map and the Hopf-Rinow theorem

● Connection between curvature and topology (e.g. Myer's theorem, Hadamard-Cartan, Klingenberg, rigidity theorems)

● Closed geodesics

● Stokes' theorem and Cohomology

● Spaces of constant curvature, Lie groups, homogeneous spaces

● Conformal geometry, geometric differential equations

● Basic notions from differential topology

### (19050)

Regular participation: at least 85% of participation in the tutorials is needed. Active participation: at least 60% of all possible points that can be earned in the homework assignements are needed.Type | Lecture |
---|---|

Instructor | Prof. Dr. Konrad Polthier, Henriette Lipschütz |

Language | English |

Credit Points | 10 |

Room | Arnimallee 6 |

Start | Apr 16, 2018 |

Time | *Lecture: Monday, 12-14, 007/008/A6, Wednesday, 12-14, 007/008/A6 *Tutorials: Friday, 10-12, 032/A6 *Exams: first July, 20th, 2018. Dates will be given on request. second: tba |

Note | The lectures and the tutorials will be held in English on request. |

## Literature

- Lee, John M., Introduction to Smooth Manifolds, Springer, 2012
- Lee, John M., Riemannian Manifolds: An Introduction to Curvature, Springer, 1997
- Kühnel, Wolfgang, Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
- O'Neill, Barret: Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983
- Guillemin, Victor and Pollack, Alan: Differential Topology, AMS Chelsea Publishing, 2010
- Hirsch, Morris: Differential Topology, Graduate Texts in Mathematics, Springer, 1997
- Kreck, Matthias: Differential Algebraic Topology, Graduate Studies in Mathematics, Band 110, AMS, 2010
- Munkres, James: Topology, Pearson New International Edition, 2013

Further Reading:

- Minimum number of charts for RP^n: http://link.springer.com/chapter/10.1007%2FBFb0085228