Weak Nearly S- and Weak Nearly 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.