String world surfaces in spaces with compact factor-manifolds

The closed string with point-like masses as the string hadron model is considered in the $D$-dimensional space $\mathcal M=R^{1,3}\times T^{D-4}$, which is the direct product of the Minkowski space and the compact manifold $T^{D-4}=S^1\times\dots\times S^1$ ($(D-4)$-dimensional torus). Exact solutions of dynamical equations are obtained; in a particular case of rotational states, they describe a uniform rotation of the system. These rotational states are classified, their physical properties are studied, and Regge trajectories are determined. Central and linear rotational states are tested for stability with respect to small disturbances. It is shown that the central rotational states are not stable if the central mass it less than some threshold value.