MSC in Mathematics, Pure Mathematics, Elective Course


 Transformation groups and symmetric spaces PM


 Dr. Balázs Csikós (associate professor)

 Dr. Gyula Lakos (teaching assistant)

 Dr. Gábor Moussong (assistant professor)

 Dr. László Verhóczki (associate professor)




 3rd semester


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.


Sigurdur Helgason: Differential geometry, Lie groups, and symmetric  and spaces. American Mathematical Society, 2001.

Glen E. Bredon: Introduction to compact transformation groups. Academic Press, New York, 1972.

form of tuition

Two hours of lecture per week.

mode of assessment

 oral exam