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

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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 1     Solutions 1

Exercise 2     Solutions 2

Exercise 3     Solutions 3

Exercise 4     Solutions 4

Exercise 5     Solutions 5

Exercise 6     Solutions 6

Exercise 7     Solutions 7

Exercise 8     Solutions 8

Exercise 9     Solutions 9

Exercise 10     Solutions 10

Exercise 11     Solutions 11

Exercise classes

GroupDayTimeRoomInstructor
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

Course feedback can be given at any point during the course. Click here.

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