401-3532-08L Differential Geometry II
Semester | Frühjahrssemester 2017 |
Dozierende | U. Lang |
Periodizität | jährlich wiederkehrende Veranstaltung |
Lehrsprache | Englisch |
Kurzbeschreibung | Introduction to Riemannian Geometry in combination with some elements of modern metric geometry. Contents: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, curvature and topology, spaces of riemannian manifolds. |
Lernziel | The aim of this course is to give an introduction to Riemannian Geometry in combination with some elements of modern metric geometry. |
Inhalt | Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form of submanifolds, riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, relations between curvature and topology, spaces of riemannian manifolds. |
Literatur | Riemannian Geometry: - M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004 - B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press 1983 Metric Geometry: - M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer 1999 - D. Burago, Y. Burago, S. Ivanov, A Course in Metric Geometry, Amer. Math. Soc. 2001 |
Voraussetzungen / Besonderes | Prerequisite is a working knowledge of elementary differential geometry (curves and surfaces in Euclidean space), differentiable manifolds, tangent and tensor bundles, and differential forms. |