SUBJECT
Title
Differential geometry II
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Differentiable manifolds. Smooth mappings between manifolds. Tangent space at a point. Tangent bundle of a manifold. Lie bracket of two smooth vector fields. Submanifolds. Covariant derivative. Parallel transport along a curve. Riemannian manifold, Levi-Civita connection. Geodesic curves. Riemannian curvature tensor field. Spaces of constant curvature. Differential forms. Exterior product. Exterior derivative. Integration of differential forms. Volume. Stokes’ theorem.
Readings
- F. W. Warner: Foundations of differentiable manifolds and Lie groups. Springer-Verlag, New York, 1983.
- M. P. do Carmo: Riemannian geometry. Birkhäuser, Boston, 1992.