  Neutron stars are supposed to be mainly formed by a neutron superfluid. The
angular momentum is given by the vortex array within the fluid, and a good
account of the observable effects is determined by its coupling with the crust.
In this article we show that the gravitational field introduces important
modifications in the vortex distribution and shape. The inertial frame dragging
on the quantum fluid produces a decrease in the vortex density, which for
realistic models is in the order of 15%. This effect is relevant for neutron
star rotation models and can provide a good framework for checking the quantum
effect of the frame dragging.
