Urs Lang: Catalogue data in Spring Semester 2020 |
| Name | Prof. Dr. Urs Lang |
| Field | Mathematik |
| Address | Professur für Mathematik ETH Zürich, HG G 27.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 60 11 |
| urs.lang@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~lang |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-3532-08L | Differential Geometry II  | 10 credits | 4V + 1U | U. Lang | |
| Abstract | 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, relations between curvature and topology, spaces of Riemannian manifolds. | ||||
| Objective | Learn the basics of Riemannian geometry and some elements of modern metric geometry. | ||||
| Literature | - 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 | ||||
| Prerequisites / Notice | Prerequisite is a working knowledge of elementary differential geometry (curves and surfaces in Euclidean space), differentiable manifolds, and differential forms. | ||||
| 401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, A. Sisto, University lecturers | |
| Abstract | Research colloquium | ||||
| Objective | |||||