Differential Geometry II (Winter 14) - Analysis and geometry on manifolds -

News:

• There will be no exercise sheet this week (January 19-24) - next sheet January 27.
• Exercise sheet 5 has been changed.
• The lecture starts at Thursday October 16, the tutorial at October 22.

Content:

Differentiable manifolds, vector bundles, differential forms, Riemannian geometry.

Course work:

There will be weekly homework assignments. To obtain the course certificate you need to get 50% of the points.

Exercise Sheets:

• 1. Exercise sheet [pdf], due October 30
• 2. Exercise sheet [pdf], due November 6
• 3. Exercise sheet [pdf], due November 13
• 4. Exercise sheet [pdf], due November 20
• 5. Exercise sheet [pdf], due November 27
• 6. Exercise sheet [pdf], due December 4
• 7. Exercise sheet [pdf], due December 11
• 8. Exercise sheet [pdf], due December 18
• 9. Exercise sheet [pdf], due January 8
• 10. Exercise sheet [pdf], due January 15
• 11. Exercise sheet [pdf], due January 22
• 12. Exercise sheet [pdf], due February 5

Literature:

• B. Andrews, Lectures on Differential Geometry, lecture notes.
• N. Hitchin, Differentiable Mannifolds, lecture notes.
• D. Ferus, Differentialgeometrie 2 (Riemannsche Geometrie), lecture notes.
• W. Ballmann, Notes on Differential Geometry, lecture notes.
• F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer 1983.
• S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer, 2004.

Further:

• J. M. Lee, Introduction to Smooth Manifolds, Springer, 2012.
• Dubrovin, Fomenko, Novikov, Modern Geometry I-III, Springer, 1990.
• J. Milnor, Topology from the Differentiable Viewpoint, The University Press of Virginia, 1965.
• M. Spivak, A comprehensive Introduction to Differential Geometry I-V, Publish or Perish 1975.

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