The aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry.
Lernziel
Riemannian Geometry, metric geometry.
Inhalt
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.
Skript
Will be made available.
Literatur
M.P. do Carmo, "Riemannian Geometry", Birkhauser, 1992
M. Bridson, A. Haefliger, "Metric Spaces of Non-Positive Curvature", Springer 1999.
Voraussetzungen / Besonderes
Prerequisite are the sections concerning manifolds and tangent bundles of the Differential Geometry I course, Fall Semester 2015.
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)