For an isometric immersion $f$ of a flat torus into the unit 3-sphere, we show that if the mean curvature of $f$ is not constant, then the immersion $f$ admits a nontrivial isometric deformation preserving the total mean curvature.
Tohoku Math. J. (2)
52(2):
283-298
(2000).
DOI: 10.2748/tmj/1178224612
