Nearly Sasakian manifolds revisited (Q2329449)

Sasakian manifolds are often considered to be the odd-dimensional analogues of Kähler manifolds. In this light D. K. Showers, K. Yano and the reviewer introduced the notion of a nearly Sasakian manifold analogous to the notion of a nearly Kähler manifold and gave a 5-dimensional example of a non-Sasakian, nearly Sasakian manifold [\textit{D. E. Blair} et al., Kōdai Math. Semin. Rep. 27, 175--180 (1976; Zbl 0328.53036)]. In [Ann. Mat. Pura Appl. (4) 197, No. 1, 127--138 (2018; Zbl 1384.53028)] the latter three authors of the present paper proved that a nearly Sasakian manifold of dimension at least 7 is Sasakian. Here the authors prove a number of new properties (often working in the nearly pseudo-Sasakian context) resulting in a more conceptual proof of the result that a nearly Sasakian manifold of dimension at least 7 is Sasakian.