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401-3532-08L  Differential Geometry II

SemesterSpring Semester 2016
LecturersM. Burger
Periodicityyearly recurring course
Language of instructionEnglish


AbstractThe aim of this course is to give an introduction to Riemannian Geometry and modern metric geometry.
ObjectiveRiemannian Geometry, metric geometry.
ContentThe 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 notesWill be made available.
LiteratureM.P. do Carmo, "Riemannian Geometry", Birkhauser, 1992

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