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Differential Geometry I

Differential geometry studies local and global properties of curved spaces.

Topics of the lecture will be:

  • Curves and surfaces in Euclidean space
  • Metrics and (Riemannian) manifolds
  • Surface tension and notions of curvature
  • Vector fields, tensors, covariant derivative
  • Geodesic curves, exponential map
  • Gauß-Bonnet theorem, curvature and topology
  • Connection to discrete differential geometry

Prerequisits: Analysis I, II and Linear Algebra I, II

(19202601)

TypeLecture with exercise session
InstructorProf. Dr. Konrad Polthier, Dr. Tillmann Kleiner
LanguageEnglish
Credit Points10
StartOct 15, 2025 | 10:15 AM
endFeb 11, 2026 | 11:45 AM
Time
  • Lecture: Monday 10:00-12:00 in A3/Hs 001 (Arnimallee 3-5) and Wednesday 10:00-12:00 in KöLu24-26/SR 006 (Königin-Luise-Straße 24-26); (starting October, 15th, 2025)
  • Exercise Sessions: (1) Monday, 8:00-10:00 and (2) Wednesday, 8:00-10:00; both in the Room A6/SR 031 (Arnimallee 6); (starting October, 22nd, 2025)
  • Exam 1: This will be determined soon...
  • Exam 2: This will be determined soon...

Info Sheet on the Tutorials:

Exercise Sheets:

Lecture Notes:

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