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Urs Lang: Catalogue data in Autumn Semester 2016

Name Prof. Dr. Urs Lang
FieldMathematik
Address
Professur für Mathematik
ETH Zürich, HG G 27.3
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 60 11
E-mailurs.lang@math.ethz.ch
URLhttp://www.math.ethz.ch/~lang
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-3531-00LDifferential 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 credits4V + 1UU. Lang
AbstractCurves 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.
ObjectiveIntroduction 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.
LiteratureDifferential 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
Differential Topology:
- Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds
- Victor Guillemin & Alan Pollack: Differential Topology
- Morris W. Hirsch: Differential Topology
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, U. Lang, University lecturers
AbstractResearch colloquium
Objective