2-type integral surfaces in \(S^ 5(1)\)
Let \(S^ 5\) be the unit hypersphere of the Euclidean 6-space \(E^ 6\). Consider \(S^ 5\) as a Sasakian manifold with the canonical contact 1- form \(\eta\). A surface \(M\) in \(S^ 5\) is called an integral surface if \(\eta\) restricted to \(M\) vanishes identically. In this paper, the authors classify integral surfaces of \(S^ 5\) which are mass-symmetric and of 2- type [in the sense of the reviewer, Total mean curvature and submanifolds of finite type (1984; Zbl 0537.53049)]. They show that a mass-symmetric 2-type integral surface \(M\) of \(S^ 5\) lies fully in \(S^ 5\) and is the product of a plane circle and a helix of order 4, or the product of two circles. Moreover, \(M\) belongs to a 1-parameter family of such surfaces. Furthermore, \(M\) is not stationary.
scientific article; zbMATH DE number 60846