We prove that any constant mean curvature embedded torus in the three dimensional sphere is axially symmetric, and use this to give a complete classification of such surfaces for any given value of the mean curvature.
"Embedded constant mean curvature tori in the three-sphere." J. Differential Geom. 99 (2) 169 - 189, February 2015. https://doi.org/10.4310/jdg/1421415560