D. Kotschick: Geometry of Manifolds I

(Differentialgeometrie I, in englischer Sprache)

• Time and place: Tu, Fr 11-13, room B 006
• Recitation classes: We 16-18, room B 006
• Contents: This is the first half of a full-year course on differentiable manifolds. We shall introduce the basic concepts used in modern geometry: manifolds, bundles, Lie groups; differential forms, distributions and integrability conditions; Riemannian metrics, connections, curvature. Further topics will be chosen mostly from Riemannian and perhaps also from symplectic geometry.
• Lecture notes
• Intended audience: This course is obligatory for all master's degree students wishing to take more advanced courses and seminars in geometry during their second year. It is also suitable for those who do not want to specialize in this area, but want to be examined in geometry to cover the pure mathematics requirement for the master's degree.
  Diplom- und Lehramts-Studenten die eine Einführung in die Differentialgeometrie hören wollen, sollten diese Vorlesung besuchen. (Bei Bedarf werden sowohl deutsche als auch englische Übungsgruppen angeboten.) Für Lehramtstudenten eignet sich diese Vorlesung für das Prüfungsgebiet Geometrie im Staatsexamen.
• Prerequisites: We shall assume familiarity wih linear algebra, multivariable calculus and point set topology.
• Main text: L. Conlon: Differentiable Manifolds  --- A first course. Birkhäuser Verlag 1993.
  Further Reading: M. H. Freedman and F. Luo: Selected Applications of Geometry to Low-Dimensional Topology. Amer. Math. Soc.
  B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry --- Methods and Applications, Vol. II, Springer Verlag 1990.
  F. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer Verlag 1983.
  S. Lang: Fundamentals of Differential Geometry. Springer Verlag 1999.
  P. Pedersen: Riemannian Geometry. Springer Verlag 1998.