  We consider a long-range interacting system of $N$ particles moving on a
spherical surface under an attractive Heisenberg-like interaction of infinite
range, and evolving under deterministic Hamilton dynamics. The system may also
be viewed as one of globally coupled Heisenberg spins. In equilibrium, the
system has a continuous phase transition from a low-energy magnetized phase, in
which the particles are clustered on the spherical surface, to a high-energy
homogeneous phase. The dynamical behavior of the model is studied analytically
by analyzing the Vlasov equation for the evolution of the single-particle
distribution, and numerically by direct simulations. The model is found to
exhibit long lived non-magnetized quasistationary states (QSSs) which in the
thermodynamic limit are dynamically stable within an energy range where the
equilibrium state is magnetized. For finite $N$, these states relax to
equilibrium over a time that increases algebraically with $N$. In the
dynamically unstable regime, non-magnetized states relax fast to equilibrium
over a time that scales as $\log N$. These features are retained in presence of
a global anisotropy in the magnetization.
