D. Kotschick: Geometry of Manifolds II

(Riemannsche Geometrie, in englischer Sprache)

• Time and place: Mo, Th 11-13, room E 47
• Recitation classes: Th 14-16, room E 47
• Contents: Lie groups and homogeneous spaces; spaces of constant curvature; the Bochner technique and some applications; structure theorems for manifolds with sectional or Ricci curvatures of a fixed sign (Myers, Synge and Cheeger-Gromoll theorems for positive curvature, Cartan-Hadamard, Cartan and Preissmann theorems for negative curvature).
• Syllabus
• Intended audience: Diplom-, Lehramts- und Master-Studenten der Mathematik und der Physik.
• Prerequisites: We shall assume only a basic knowledge of differentiable manifolds. It is not necessary to have attended Geometry of manifolds I, which covered more than enough background material for this course.
• Main text: P. Pedersen: Riemannian Geometry. Springer Verlag 1998.
  Other recommended reading: R. L. Bishop and R. J. Crittenden: Geometry of Manifolds. 1964, reprinted 2001 by AMS Chelsea Publishing.
  F. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer Verlag 1983.
  S. Lang: Fundamentals of Differential Geometry. Springer Verlag 1999.