2-Type Integral Surfaces in $S^5(1)$

Abstract

The main purpose of this paper is to classify integral surfaces of the unit sphere $S^5(1)$ which are mass-symmetric and of 2-type. If we consider $S^5(1)$ as a Sasakian manifold, then we prove that a mass-symmetric 2-type integral surface of $S^5(1)$ lies fully in $S^5(1)$ and is the product of a plane circle and a helix of order 4 or the product of two circles.