Submanifolds with parallel mean curvature vector in η-Einstein Sasaki manifold

Abstract

In this note, we prove that for a 3-dimensional submanifold in an η-Einstein 5-Sasaki manifold with Einstein constant a≥4, if the Reeb vector field is tangent to the submanifold and it has parallel mean curvature form, then it is a slant submanifold. Furthermore, if a>4, then it is either an invariant submanifold or an anti-invariant submanifold.