Riemannian geometry, spring 2016
Teacher: Ilkka Holopainen
Scope: 10 cr
Type: Advanced studies
Teaching: Weeks 3-9 and 11-18, Wednesday 10-12 and Thursday 10-12 in room C123.
Topics:
- Differentiable manifolds (brief review if needed)
- Riemannian metrics
- Connections
- Geodesics
- Curvature
- Jacobi fields
- Curvature and topology
- Comparison geometry
- The sphere theorem (optional)
Prerequisites: Vector analysis, topology, linear algebra, some knowledge on smooth manifolds
(like the course "Introduction to differential geometry") and on differential equations.
News
Teaching schedule
Weeks 3-9 and 11-18, Wednesday 10-12 and Thursday 10-12 in room C123.
First lecture on Wednesday, January 20.
Last lecture on Thursday, May 5.
Easter holiday 24.3.-30.3.
Exams
The course can be passed by an exam. First possibilities are on May 18 or May 24.
Course material
- DoCarmo: Riemannian geometry, Birkhäuser, 1992
- Lee: Riemannian manifolds, An Introduction to Curvature, Springer, 1997
Lecture notes (first 101 pages):
Ilkka Holopainen and Tuomas Sahlsten: Riemannian Geometry
Registration
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Exercises
Assignments and solutions
Exercise classes
| Group | Day | Time | Room | Instructor |
|---|---|---|---|---|
| 1. | Tuesday | 12-14 | B321 | Esko Heinonen |
You will get extra credit points by solving the home work exercises:
25% = +1p, 35% = +2p, 45% = +3p, 55% = +4p, 65% = +5p ja 75% = +6p.
Course feedback
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