A note on Chen's basic equality for submanifolds in a Sasakian space form

Abstract

It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form M˜(c) of constant φ-sectional curvature c<1, with the structure vector field ξ tangent to M, satisfies Chen's basic equality if and only if it is a 3-dimensional minimal invariant submanifold.