Riemannian geometry, fall 2010

Lecturer

Ilkka Holopainen

Scope

10 cu.

Type

Advanced studies

Prerequisites

Vector analysis, topology, linear algebra, some knowledge on smooth manifolds
 (like the course "Johdatus diferentiaaligeometriaan") and on differential equations.

Lectures

Weeks 36-42 and 44-50, Tue 12-14, Thur 10-12 in room C123.

Exercise groups

Friday, 12-14 in room C124.

Exams

The course can be passed by an exam. Extra credit from home work classes.

Content

• Differentiable manifolds (brief review)
• Riemannian metrics
• Connections
• Geodesics
• Curvature
• Jacobi fields
• Curvature and topology
• Comparison geometry
• The sphere theorem

Bibliography

• 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

Registration

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Home work assignments and solutions