Geometric phase related to point-interaction transport on a magnetic Lobachevsky plane

We consider a charged quantum particle living in the Lobachevsky plane and interacting with a homogeneous magnetic field perpendicular to the plane an d a point interaction which is transported adiabatically along a closed loo p cal C in the plane. We show that the bound-state eigenfunction acquires a t that the Berry phase equal to 2 pi times the number of the flux quanta th rough the area encircled by cal C.