2-type surfaces in \(S^ 3\) (Q1093183)

It is known that a compact surface in a unit hypersphere \(S^ 3\) of a Euclidean 4-space is mass-symmetric and of 2-type if and only if it is the product of two plane circles with different radii [the reviewer, Total mean curvature and submanifolds of finite type, Series in Pure Mathematics, Vol. 1, Singapore: World Scientific Publishing Co. XI, 352 p. (1984; Zbl 0537.53049)]. The main purpose of this article is to show that a compact 2-type surface in \(S^ 3\) is always mass-symmetric.