Lecture:  Riemannian Geometry (Master) - Winter term 2020/21
Instructor: Sara Azzali
Exercise Class: Sara Azzali
Aim: This course will be an introduction to global Riemannian geometry. We will develop techniques that permit to relate local assumptions on a Riemannian manifold (such as curvature conditions) with the global structure of the space (for instance topological properties).
Content: The topics of this course include:
  • Geodesics and their local minimising property
  • Metric structure and the Hopf--Rinow theorem
  • Jacobi fields, first and second variation
  • Cartan--Hadamard theorem
  • Bonnet--Myers theorem
  • Spaces of constant curvature
  • Synge theorem, comparison theorems
  • Curvature and the growth of the fundamental group
Prerequesites: Basic knowledge of differential geometry as given in the differential geometry course of the bachelor (manifolds, vector fields, differential forms, vector bundles and connections, Riemannian manifolds, the Levi-Civita connection, curvature). Notes of the introductory course in differential geomtery by D. Lindemann in the Summer Term can be found here
Literature: Do Carmo, Riemannian Geometry,
Gallot, Hulin, Lafontaine, Riemannian Geometry,
O'Neill, Semi-Riemannian Geometry,
When and where: Due to the current pandemic, in digital form.
Videolectures are posted weekly on Lecture2Go and are accessible from Moodle.
Exercice classes: on Big Blue Button
Office hours: Fridays 12.15-13.45 on Big Blue Button: https://lernen.min.uni-hamburg.de/mod/bigbluebuttonbn/view.php?id=28248
or by appointment (do not hesitate to contact me per email sara.azzali (at) uni-hamburg.de)
Exam: The final exam for this course is an oral exam at the end of term.