Differential Geometry II/Differentialgeometrie II

Summer term 2024

Prof. Bernd Ammann, Office M 119

Current Announcements

Please register on GRIPS. We will send email announcements over this system.


This course is "English on demand". This means the language will be decided during the first week of the lecture. If there is at least one non-German-speaking person in the audience who is sincerely following the lecture, then the lecture will be given in English.

Recommended previous knowledge

Content of the Lecture

This lecture establishes relations between the topology of a smooth manifold and its curvature properties. This is a central question within Riemannian geometry. Probably, lecture notes will be written for this lecture.

The lecture builds on the lecture Differential Geometry I, where we have started to treat the first such relations. The lecture shall lead to a good understand about the consequences of positive or negative curvature, for various notions of curvature (sectional, Ricci, scalar). We list some examples of relations in the focus of the lecture, including some relations partially treated at the end of Differential Geometry I. We will probably not have the time to cover all of them.

Other possible topics of the lecture are Lie groups and vector bundles including characteristic classes. The precise content of the lecture will depend on the previous knowledge and the interests of the audience.


Exercise group

There will be a weekly exercise sheet and a weekly exercise group. The exercise group is currently planned for Thursday 10-12 (the time and day of week might change!)..

Exercise Sheets

and finally all exercise sheets in one pdf file.

Links to related web pages


The examination is an oral examination of about 30 minutes.

Formal criteria/Kriterien für Leistungsnachweise

We refer to the KVV.

Bernd Ammann, 26.01.2024
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