discipline 
MSC in Mathematics, Pure Mathematics,
Elective Course

subject 
Transformation
groups and symmetric spaces PM

lecturers 
Dr. Balázs Csikós (associate professor) Dr. Gyula Lakos (teaching assistant) Dr. Gábor Moussong (assistant professor) Dr. László Verhóczki (associate professor) 
credits 
2 
period 
3rd semester 
curriculum 
Smooth left action of a Lie group on a
differentiable manifold. Orbits, isotropy subgroups. Homogeneous spaces as
special differentiable manifolds, left invariant Riemannian metrics. Lie
group structure of the isometry group of a Riemannian manifold.
Characterization of Riemannian locally symmetric spaces by the curvature tensor.
Compact Lie groups as symmetric spaces. General construction of symmetric
spaces. Expression of the curvature tensor by the Lie brackets.
Classification of semisimple symmetric spaces. 
literature 
Sigurdur Helgason: Differential geometry, Lie
groups, and symmetric and spaces.
American Mathematical Society, 2001. Glen E. Bredon: Introduction to compact
transformation groups. Academic Press, 
form of tuition 
Two hours
of lecture per week. 
mode of assessment 
oral exam 