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401-3532-08L  Differential Geometry II

SemesterFrühjahrssemester 2016
DozierendeM. Burger
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThe aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry.
LernzielRiemannian Geometry, metric geometry.
InhaltThe 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.
SkriptWill be made available.
LiteraturM.P. do Carmo, "Riemannian Geometry", Birkhauser, 1992

M. Bridson, A. Haefliger, "Metric Spaces of Non-Positive Curvature",
Springer 1999.
Voraussetzungen / BesonderesPrerequisite are the sections concerning manifolds and tangent bundles of the Differential Geometry I course, Fall Semester 2015.