Home

Research

Teaching/Supervision

Seminars

Links

Differential Geometry, Summer Semester 2026

This course is the first course in differential geometry. This page will contain all the information related to the course.

Course Outline


Moodle (key: see the course outline above) Please join Moodle for uploading your solutions to the problem sets and for other communications.


Lectures: Mondays & Thursdays 10:15-11:45 in MIN-F Hörsaal 7 (Note the building).


Exercise sessions: Thursdays 14:15-15:45 in MIN-F SemRm 3.4. (Note the different classroom).
Office Hours: Tuesdays 14:00-15:00 in Room 320, Geomatikum.

Announcements
  • The first problem session will be on April 23rd 2026.
  • There will be no lectures, problem sessions or office hours in the week of 25th-29th May 2026. I will upload a video lecture (and notes) for one of the missed lectures and I will take the problem session on Thu. 4th June 2026 as a lecture to make-up for the other missed lecture.
  • Problem Set 5 will be uploaded on June 4th and will be discussed in the problem session on June 11th 2026.


Lecture Notes

I'll upload the lecture notes here. The notes will be in both English and German.

Lecture 1 - Topological manifolds and examples/Topologische Mannigfaltigkeiten und Beispiele

Lecture 2 - Atlas and smooth structures/Atlas und glatte Strukturen

Lecture 3 - Examples of smooth manifolds/Beispiele für glatte Mannigfaltigkeiten

Lecture 4 & 5 - Smooth maps and tangent spaces/Glatte Abbildungen und Tangentialräume

Lecture 6 - Derivations and tangent vectors/Derivations und Tangentialvektoren

Lecture 7 - Derivations, immersions and submersions/Derivations, immersions und submersions

Lecture 8 - Constant Rank theorem/Rangsatz

Lecture 9 - Submanifolds/Untermannigfaltigkeiten

Lecture 10 - Vector fields/Vektorfelder

Lecture 11 - Lie bracket and its properties/Lie-Klammern und ihre Eigenschaften

Lecture 12 - Integral curves/Integralkurven (Hand-written notes during the video lecture)

Lecture 13 - Flows of vector fields/Flüsse von Vektorfeldern

Lecture 14 & 15 - Flows, Lie derivatives/Flüsse, Lie-Ableitungen



Problem sets

Problem sets will be posted here (almost) weekly on Thursdays (starting 16th April 2026) and will be discussed in the problem sessions. It is highly recommended that you try to attempt all the problems. This will be beneficial to your understanding of the course material.

Problem Set 1 (due on 23.04.2026)

Problem Set 2 (due on 30.04.2026)

Problem Set 3 (due on 07.05.2026)

Problem Set 4 (due on 21.05.2026)

Problem Set 5 (due on 11.06.2026)