From 2 November 2020, the autumn semester 2020 will take place online. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers via e-mail.
The aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry.
Objective
Riemannian Geometry, metric geometry.
Content
The aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry. We will present the basics on affine and riemannian connections, discuss existence and properties of geodesics; then we proceed to the central concept of riemannian curvature tensor and its various avatars, like sectional curvature and scalar curvature. We will then move to Topogonov's comparison theorems. This constitutes the bridge with metric geometry and the modern notion of negative curvature, which applies to singular spaces, and constitutes the topic of the second part of this course.
Lecture notes
Will be made available.
Literature
M.P. do Carmo, "Riemannian Geometry", Birkhauser, 1992
M. Bridson, A. Haefliger, "Metric Spaces of Non-Positive Curvature", Springer 1999.
Prerequisites / Notice
Prerequisite are the sections concerning manifolds and tangent bundles of the Differential Geometry I course, Fall Semester 2015.
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course