Differential Geometry II (Winter 18) – Analysis and geometry on manifolds –

This course is a BMS basic course and the lectures will be in English. Please feel free to ask any questions (and to turn in any work) in English or German.

News

• Corrected the second exercise of sheet 12.
• The lecture starts on Tuesday October 16.
• Depending on the number of students one or two tutorials will be offered.

Contents

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

Homework

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

Homework should be turned in by groups of two students. To get a certificate for the tutorial and qualify to take the oral exam at the end of the semester, you need to satisfactorily complete 50% of the homework assignments.

Material

Lecture notes:

• Script 'Analysis and geometry on manifolds' (Notes from the course in winter 2016, revised version by Oliver Gross)

If you find mistakes or you have some comments please send an email to Felix.

Literature:

• Burstall, Basic Riemannian geometry in Spectral Theory and Geometry, L.M.S. Lect. Note Series 273, C.U.P. (1999), pages 1-29, [pdf]
• Petersen, Manifold theory, [essay]
• Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94, Springer
• Milnor, Topology from the Differentiable Viewpoint, U P Virginia

Further excellent notes on differential geometry can be found on Werner Ballmann's homepage.