D. E. Blair, D. K. Showers, and K. Yano introduced the concept of nearly Sasakian structure as an odd-dimensional counterpart of the nearly Kähler structure in Blair et al. (Kodai Math Sem Rep 27:175–180, 1976) and they proved that a normal nearly Sasakian structure is Sasakian. A remarkable example of nearly Sasakian manifold is the 5-sphere as totally umbilical hypersurface of \(S^{6}\) endowed with the almost contact structure induced by the well-known nearly Kähler structure of \(S^{6}\) . Many authors studied these structures.