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Riemannian Geometry, University of Fribourg 2016/17

Date Lecture notes Exercises
23 Sep Smooth manifolds and smooth maps, tangent vectors. Solve one of the Exercises from Sections 1.1 and 1.2.
30 Sep Commutator of vector fields, differential 1-forms. Exercises 1 and 2 from the file above.
7 Oct Differential k-forms, exterior derivative. Exercises 3 and 4.
14 Oct Exterior derivative, volume forms. Exercise 5.
21 Oct Integration. Exercises 6 and 7.
28 Oct Tensors. Exercises 9 and 10.
4 Nov Trace and contraction, tensor fields, interior product. Exercises 11, 12, and 13.
11 Nov Repetition. Exercise 14.
18 Nov Products, quotients, immersions, submersions. Exercise 15.
25 Nov Lie derivative. Exercise 16.
2 Dec Covariant derivative. Exercises 18 and 19.
9 Dec Riemannian metric. Exercise 20.
16 Dec Levi-Civita connection. Exercises 21 and 22.
23 Dec Levi-Civita connection on a submanifold. Exercises 23 and 24.