  Weak contact metric manifolds, i.e., the linear complex structure on the
contact distribution is replaced by a nonsingular skew-symmetric tensor,
defined by the author and R. Wolak, allowed us to take a new look at the theory
of contact manifolds. In this paper, we continue our study, see
arXiv:2312.11411, of a structure of this type, called a weak nearly Sasakian
structure, and prove two theorems characterizing Sasakian manifolds. Our main
result generalizes the theorem by A. Nicola - G. Dileo - I. Yudin (2018) and
provides a new criterion for a weak almost contact metric manifold to be
Sasakian.
