Department of Mathematics

Differential Geometry I

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Check in the VVZ for a current information.

Professor: Prof. Dr. Tom Ilmanen
Lectures: Monday 13-15 in HG G 3
  Wednesday 13-15 in HG G 3
First exercise session: Wednesday, September 24, or Friday, September 26
Exercises: The details are here.
Assistants: Nag Panchali ( Wednesday 15-17 HG G 26.1
  Charel Antony Wednesday 15-17 HG G 26.5
  Alexandru Paunoiu
Wednesday 15-17 LEE C 114
  Katharina Kusejko
Friday 08-10 HG F 26.5
Coordinator: Claudio Sibilia  
Year: 3., 4., graduate
Prerequisites: Analysis I+ II, Algebra I, Topologie (some), Mass und Integral (some).
Language: English
Skript: For an unofficial script from Fall 2005, see VMP mitschriften: Differentialgeometrie=> Ilmanen
Topics in Fall 2014: manifolds(intrinsic and extrinsic viewpoints), immersion and submersions, Lie brackets, Lie derivatives and flows, Riemannian metrics, geodesics, covariant derivatives, tensor and vector bundles, Riemannian curvature(intrinsic curvature), second foundamental form (extrinsic curvature), lots of examples,...
Bibliography: Lee, Riemannian Manifolds-An Introduction to Curvature, (required)
  Lee, Introduction to smooth manifolds, (recommended)
  Do Carmo, Riemannian Geometry, (recommended)
  Morgan, F. Riemannian Geometry-A Beginner's Guide (very intuitive introduction to curvature), (recommended)
Additional sources: Lee, Introduction to topological manifolds ( topological spaces and topological manifolds up to the fundamental group and covering spaces),
  Milnor, Topology from the differential point of view, (Differential topology)
  Guillemin and Pollack, Differential Topology, Chap 1 (Differential topology)
  Milnor, Morse Theory, part II (thumbnail introduction to connections, curvature, geodesics, Jacobi fields, and the Index Theorem)
  Spivak, Differential Geometry, vols I and II (chatty and thorough; vol II, Chap 4 contains an analysis of the Rieman's original essay "On the Hypotheses that lie at the Foundations of Geometry")
  Gallot, Hulin, Lagonatine Riemannian Geometry, (Advanced and pithy, lots of information)
  Hsiang, Lie groups, (a beautiful "thin" book)
  All this books are avaible at the ETH library. For more informations click here.
Topics Book(Chapter)
Introduction, curves, surfaces Lee/Morgan
Differentiable manifolds DoCarmo 0

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