  We investigate the metastability of a ferromagnetic spin-1 Bose-Einstein
condensate confined in a quasi-one-dimensional rotating ring trap by solving
the spin-1 Gross-Pitaevskii equation. We find analytical solutions that exhibit
spin textures. By performing linear stability analysis, it is shown that the
solutions can become metastable states. We also find that the number of
Nambu-Goldstone modes changes at a certain rotation velocity without changing
the continuous symmetry of the order parameter.
