Prof. D. Kotschick: Riemannian Geometry

• Time and place: Tue 10-12 B 006, Thu 10-12 B 004
• Exercise classes
• Summary: We will study the geometry of Riemannian manifolds. Topics covered include: geodesics and the metric space structure of Riemannian manifolds, including criteria for completeness (Hopf-Rinow theorem), the different notions of curvature (sectional, Ricci and scalar), spaces of constant curvature, relationships between curvature and topology (theorems of Bonnet-Myers, Cartan-Hadamard, Preissman etc.), volume growth in Riemannian covering spaces.
  
• Intended audience: Master students of mathematics and/or physics.
• Prerequisites: We will assume familiarity with the basic theory of smooth manifolds. For example, the course on differential geometry last semester covered more than is needed.
• References:
  I. Chavel: Riemannian Geometry -- A modern introduction, Cambridge UP 1993
  M. P. do Carmo: Riemannian Geometry, Birkhäuser Verlag 1992
  S. Gallot, D. Hulin, J. Lafontaine: Riemannian Geometry, Springer Verlag 1987, 1990