Morse index of constant mean curvature tori of revolution in the   3-sphere
  We compute lower bounds for the Morse index and nullity of constant mean curvature tori of revolution in the three-dimensional unit sphere. In particular, all such tori have index at least five, with index growing at least linearly with respect to the number of the surfaces' bulges, and the index of such tori can be arbitrarily large. 
Wayne Rossman, Nahid Sultana