Department Mathematik
print
Navigationspfad
Inhaltsbereich

D. Kotschick: Differenzierbare Mannigfaltigkeiten (BA) / Differential Geometry (TMP)

  • Time and place: Mo, We 10-12, room B 004
  • Recitation classes: Mo 14-16, room 204 (Schellingstr. 5) and We 12-14, room B 004
  • Contents: We shall introduce the basic concepts used in modern geometry: manifolds, vector bundles, Lie groups and Lie algebras; vector fields and flows; differential forms, distributions and integrability conditions; Riemannian metrics, connections, curvature.
  • Lecture notes
  • Intended audience: This course is obligatory for all Bachelor and all TMP students wishing to take further courses in geometry and/or topology later on. It is also suitable for those who do not want to specialize in this area, but want to learn the basics for use in physics or in other areas of mathematics.
    Bachelor-, 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 with linear algebra, multivariable calculus and point set topology.
  • Main text: L. Conlon: Differentiable Manifolds  --- A first course. Birkhäuser Verlag 1993. (The second, expanded, edition of this book does not have the subtitle "A first course'' any more; of course you can use the second edition if you like.)
    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.
    S. Morita: Geometry of Differential Forms. Amer. Math. Soc. 2001.
    F. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer Verlag 1983.
    S. Lang: Fundamentals of Differential Geometry. Springer Verlag 1999.

  • Makeup exam (Nachklausur): The makeup exam takes place on Friday, 16 April 2010, 10 AM - 12 noon, in room A125 at Geschwister-Scholl Platz 1 (Hauptgebäude der LMU). Please bring your student id, regular id, and make sure you arrive well before 10:15. Please take a seat with plenty of space around you.