Tom Ilmanen: Katalogdaten im Herbstsemester 2023 |
| Name | Herr Prof. Dr. Tom Ilmanen |
| Lehrgebiet | Mathematik |
| Adresse | Professur für Mathematik ETH Zürich, HG G 62.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 54 43 |
| Fax | +41 44 632 14 04 |
| tom.ilmanen@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~ilmanent |
| Departement | Mathematik |
| Beziehung | Ordentlicher Professor |
| Nummer | Titel | ECTS | Umfang | Dozierende | |||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-3531-00L | Differential Geometry I  Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar. Die Kategoriezuordnung können Sie in diesem Fall nicht selber in myStudies vornehmen, sondern Sie müssen sich dazu nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (www.math.ethz.ch/studiensekretariat) wenden. | 9 KP | 4V + 1U | T. Ilmanen | |||||||||||||||||||||||
| Kurzbeschreibung | Introduction to differential manifolds and differential geometry. Introduce the language, tools, and basic results of differentiable manifolds, tensors, Riemannian geometry, and related geometric structures. Relate geometric intuition to formulas involving curvature, derivatives and tensors. | ||||||||||||||||||||||||||
| Lernziel | Learn to compute, describe, prove, and solve problems in the language of differential geometry. | ||||||||||||||||||||||||||
| Inhalt | Submanifolds of R^n, immersions, submersions, and embeddings, Sard's Theorem, abstract differentiable manifolds, charts, vector fields and flows, vector bundles, tensor fields, covariant derivatives, parallel transport, Riemannian metrics, geodesics, Riemann curvature tensor. Complete manifolds, Hopf-Rinow theorem. Many examples including curves, surfaces, hyperbolic space, S^3, the unit quaternions, the Gauss-Bonnet theorem, etc. | ||||||||||||||||||||||||||
| Literatur | John M. Lee: Introduction to Smooth Manifolds John M. Lee: Introduction to Riemannian Manifolds This following books were inherited from before. The only one I know is DoCarmo. - Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces - S. Montiel, A. Ros: Curves and Surfaces - S. Kobayashi: Differential Geometry of Curves and Surfaces - Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten - Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds | ||||||||||||||||||||||||||
| Kompetenzen |
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| 401-5350-00L | Analysis Seminar | 0 KP | 1K | F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, T. Ilmanen, L. Kobel-Keller, S. Mayboroda, T. Rivière, J. Serra, Uni-Dozierende | |||||||||||||||||||||||
| Kurzbeschreibung | Research colloquium | ||||||||||||||||||||||||||
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