Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifolds

Quasi contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of the contact metric manifolds. Weak almost contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, were defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi contact metric manifolds. Our main results generalize some well known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure.