Characterization of Sasakian manifolds

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