Geodesic
A Version of the Ruh--Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$
Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 92-105.

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We study a version of the Gauss map $g\ :M^2\to S^2$ for a surface $M^2$ immersed in $S^3$ and prove an analog of the Ruh–Vilms theorem which states that this map is harmonic if $M^2$ has a constant mean curvature. As a corollary, we conclude that an embedded flat torus $T^2$ with constant mean curvature is a spherical Delonay surface. 
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L. A. Masal'tsev. A Version of the Ruh--Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$. Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 92-105. http://geodesic.mathdoc.fr/item/MZM_2003_73_1_a7/

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