Geometry of a two-spin quantum state in evolution

We study the quantum evolution of a two-spin system described by the isotropic Heisenberg Hamiltonian in the external magnetic field. It is shown that this evolution happens on a two-parametric closed manifold. The Fubini-Study metric of this manifold is obtained. It is found that this is the metric of the torus. The entanglement of the states which belong to this manifold is investigated.