Weak Nearly \({\mathcal S}\)- and Weak Nearly \({\mathcal C}\)-Manifolds

The recent interest in geometers in the f -structures of K. Yano is motivated by the study of the dynamics of contact foliations, as well as their applications in theoretical physics. Weak metric f -structures on a smooth manifold, recently introduced by the author and R. Wolak, open a new perspective on the theory of classical structures. In this paper, we define structures of this kind, called weak nearly S - and weak nearly C -structures, study their geometry, e.g., their relations to Killing vector fields, and characterize weak nearly S - and weak nearly C -submanifolds in a weak nearly Kähler manifold.