discipline 
MSC in Mathematics, Pure Mathematics,
Elective Course

subject 
General Structures
in Differential Geometry

lecturers 
Dr. Balázs Csikós (associate professor) Dr. Gyula Lakos (assistant) Dr. Gábor Moussong (assistant professor) Dr. László Verhóczki (associate professor) 
credits 
2 
period 
4th semester 
curriculum 
Optional topics: Hyperbolic manifolds. The Mostow rigidity theorem.
Hyperbolic geometry in the theory of 3dimensional manifolds. Elements of the
ThurstonJorgensen theory. Symplectic manifolds. Darboux theorem. Poisson
manifolds. Symplectic structure on the orbits of coadjoint representations.
Geometric quantization of symplectic manifolds. The orbit method. Distributions. Frobenius theorem. Lagrange
functions, and EulerLagrange equation. Noether’s theorem. Legendre
transformation. Connection between the Hamiltonian and Lagrange formalism. Clifford and spin structures. Dirac operators.
Index theorems. The heat equation method. Pseudodifferential operators.
Ellipticity, Fredholm properties. 
literature 

form of tuition 
Two hours
of lecture per week. 
mode of assessment 
oral exam 