Winter 11/12
Lecturers: |
Prof. Dr. K. Polthier |
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Dr. C. Lange |
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Dipl.-Math. St. W. von Deylen |
Classes: |
Tue 10-12 - Room SR 032 in Arnimallee 6 |
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Thu 10-12 - Room SR 032 in Arnimallee 6 |
Tutorial: |
Wed 10-12 - Room SR 031 in Arnimallee 6 (Lange) |
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Thu 16-18 - Room SR 032 in Arnimallee 6 (von Deylen)
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tutorials on thursday are in german
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Content
Differential geometry studies the local and global properties of curved
spaces. Topics of the lecture will be: curves and surfaces in Euclidean
space, differentiable manifolds, vector bundles, especially the tangent
bundle, tensors, Riemannian manifolds, connections, curvature tensors, the
geometry of submanifolds, geodesics, and some theorems from global
differential geometry.
Prerequisites
Basic linear algebra, basic calculus.
Exercise sheets
Additional Material
Written Exam
To qualify for the written exam, you have to attend one of the two tutorials regularly,
participate actively, and achieve at least 50% of the points for the homework assignments.
Date of 1st written exam: February 7th, 2012.
Date of 2nd written exam: April 2nd, 2012, 10 a. m. (sharp) in Room 032. (every qualified student is allowed to attend, independent of the 1st exam's result)
Main Textbooks
- W. Kühnel
Differential Geometry: Curves - Surfaces - Manifolds
Oxford University Press
german edition:
Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten, Vieweg Verlag
- M. P. doCarmo
Differential Geometry of Curves and Surfaces
Prentice Hall
german edition:
Differentialgeometrie von Kurven und Flächen, Vieweg Verlag
Further Textbooks (additional topics etc.)
- J.-H. Eschenburg, J. Jost
Differentialgeometrie und Minimalflächen
Springer Verlag
- A. Gray
Modern Differential Geometry of Curves and Surfaces with Mathematica
CRC Press
german edition:
Differentialgeometrie. Klassische Theorie in moderner Darstellung, Spektrum Verlag
- D. Hilbert, S. Cohn-Vossen
Anschauliche Geometrie, Springer Verlag
english edition:
Geometry and the Imagination
AMS Chelsea Publishing
- J. Lee
Introduction to Smooth Manifolds
Springer Verlag
- Th. Bröcker, K. Jänich
Einführung in die Differentialtopologie
Springer Verlag
- Ch. Bär
Elementare Differentialgeometrie
de Gruyter
- W. Blaschke
Vorlesungen über Differentialgeometrie
Springer Verlag
- E. Brieskorn, H. Knörrer
Ebene algebraische Kurven
Birkhäuser