Riemannian geometry, fall 2010
Vector analysis, topology, linear algebra, some knowledge on smooth manifolds
(like the course "Johdatus diferentiaaligeometriaan") and on differential equations.
Weeks 36-42 and 44-50, Tue 12-14, Thur 10-12 in room C123.
Friday, 12-14 in room C124.
The course can be passed by an exam. Extra credit from home work classes.
- Differentiable manifolds (brief review)
- Riemannian metrics
- Jacobi fields
- Curvature and topology
- Comparison geometry
- The sphere theorem
- DoCarmo: Riemannian geometry, Birkhäuser, 1992
- Lee: Riemannian manifolds, An Introduction to Curvature, Springer, 1997
and (hand written) lecture notes: Holopainen: Differential Geometry (1999, 2001).
Lecture notes (first 101 pages, not proof-read): RiemannGeo.pdf
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