Ricci curvature of integral submanifolds of an \(f.p.k.\)-space form (Q464212)

Relationships between the Ricci curvature and the squared mean curvature for integral submanifolds of an \(f.p.k.\)-space form by a basic inequality, are studied. Let us recall that in the class of \(f\)-structures introduced by \textit{K. Yano} [Tensor, New Ser. 14, 99--109 (1963; Zbl 0122.40705)], particularly interesting are the so-called \(f\)-structures with complemented frames, also called globally framed \(f\)-structures or \(f\)-structures with parallelizable kernel (briefly \(f.p.k.\)-structures). The author shows that if an integral submanifold of maximum dimension of an \(f.p.k.\)-space form satisfies the equality case, then it must be minimal.