Urs Lang: Catalogue data in Autumn Semester 2016
|Name||Prof. Dr. Urs Lang|
Professur für Mathematik
ETH Zürich, HG G 27.3
|Telephone||+41 44 632 60 11|
|401-3531-00L||Differential Geometry I|
This course counts as a core course in the Bachelor's degree programme in Mathematics. Holders of an ETH Zurich Bachelor's degree in Mathematics who didn't use credits from neither 401-3531-00L Differential Geometry I nor 401-3532-00L Differential Geometry II for their Bachelor's degree still can have recognised this course for the Master's degree.
Furthermore, at most one of the three course units
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.
|10 credits||4V + 1U||U. Lang|
|Abstract||Curves in R^n, inner geometry of hypersurfaces in R^n, curvature, Theorema Egregium, special classes of surfaces, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, tangent bundle, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.|
|Objective||Introduction to elementary differential geometry and differential topology.|
|Content||- Differential geometry in R^n: theory of curves, submanifolds and immersions, inner geometry of hypersurfaces, Gauss map and curvature, Theorema Egregium, special classes of surfaces, Theorem of Gauss-Bonnet, Poincaré Index Theorem.|
- The hyperbolic space.
- Differential topology: differentiable manifolds, tangent bundle, immersions and embeddings in R^n, Sard's Theorem, transversality, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.
|Literature||Differential Geometry in R^n:|
- Manfredo P. do Carmo: Differential geometry of curves and surfaces
- Wolfgang Kühnel: Differentialgeometrie. Curves-surfaces-manifolds
- Christian Bär: Elementary differential geometry
- Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds
- Victor Guillemin & Alan Pollack: Differential Topology
- Morris W. Hirsch: Differential Topology
|401-5530-00L||Geometry Seminar||0 credits||1K||M. Burger, M. Einsiedler, U. Lang, University lecturers|