  We study the evolution of a spin-s system described by the long-range zz-type
Ising interaction. The Fubini-Study metric of the quantum state manifold
defined by this evolution is obtained. We explore the topology of this manifold
and show that it corresponds to a sphere. Exploration of the Riemannian
curvature allows us to determine the manifold geometry. Also we calculate the
speed of evolution of the system and represent the curvature by means of this
speed. This is important for an experimental measurement of the curvature. The
conditions for achieving the minimal and maximal values of the speed of
evolution are obtained. Also we examine the geometry of state manifold and
speed of evolution of spin system in the thermodynamic limit. We propose the
physical system of methane molecule for application of our considerations.
Finally, we study the influence of an external magnetic field on the metric of
state manifold and on the speed of evolution. In this case we obtain the
conditions for achieving the minimal possible speed of evolution. For some
predefined initial states the orientations of magnetic fields to reach the
minimal and maximal values of the speed are found.
