Spring 2018

- Lecturer
- Prof. Dr. Alessandra Iozzi
- Coordinator
- Yannick Krifka (E-mail)

- Generalities on symmetric spaces: locally and globally symmetric spaces, groups of isometries, examples.
- Symmetric spaces of non-compact type: flats and rank, roots and root spaces.
- Iwasawa decomposition, Weyl group, Cartan decomposition.
- Hints of the geometry at infinity of \( \text{SL}(n,\mathbb{R})/\text{SO}(n,\mathbb{R}) \).

Learn the basics of symmetric spaces.

The exercise sheets will be posted below.

Exercise Sheet | Solution | Comment |
---|---|---|

Exercise Sheet 1 | Solution 1 | |

Exercise Sheet 2 | Solution 2 | |

Exercise Sheet 3 | Solution 3 | |

Exercise Sheet 4 | Solution 4 | |

Exercise Sheet 5 | Solution 5 |

time | room |
---|---|

Tue 10-12 am | HG D 5.2 |

Thu 08-10 am | HG G 5 |

About every second week there will be an exercise class led by Yannick Krifka instead of a lecture on Thursday.

However, there will be some irregularities that are being displayed in the following colour coded table:

Tuesday | Thursday |
---|---|

Feb 20 | Feb 22 |

Feb 27 | Mar 1 |

Mar 6 | Mar 8 |

Mar 13 | Mar 15 |

Mar 20 | Mar 22 |

Mar 27 | Mar 29 |

Apr 3 | Apr 5 |

Apr 10 | Apr 12 |

Apr 17 | Apr 19 |

Apr 24 | Apr 26 |

May 1 | May 3 |

May 8 | May 10 |

May 15 | May 17 |

May 22 | May 24 |

May 29 | May 31 |

Legend: lecture, exercise class, holiday.

You can find notes on a previous course on symmetric spaces here.

Notes on this course will be uploaded here.

Apart from these notes the following books might be of interest to you.

- A. Borel: "Semisimple groups and Riemannian symmetric spaces" (Springer, 1998)
- M. Bridson, A. Haefliger: "Metric spaces of non-positive curvature" (Springer, 1999)
- M. do Carmo: "Riemannian geometry" (BirkhĂ¤user, 1992)
- P. Eberlein: "Geometry of nonpositively curved manifolds" (Chicago University Press, 1996)
- S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, 1978)
- S. Kobayashi, K. Nomizu: "Foundations of differential geometry. Vol. II" (Wiley, 1996)