This article is cited in 3 papers

A Version of the Ruh–Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$

L. A. Masal'tsev

V. N. Karazin Kharkiv National University

Abstract: 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.

UDC: 514

Received: 22.06.2001

DOI: 10.4213/mzm172

 English version: Mathematical Notes, 2003, 73:1, 85–96

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