Contact Self-Dual Geometry of Quasi-Sasakian 5-Manifolds

We construct a self-dual geometry of quasi-Sasakian 5-manifolds. Namely, we intrinsically define the notion of contact conformally semiflat (i.e., contact self-dual or contact anti-self-dual) almost contact metric manifolds and also obtain a number of results concerning contact conformally semiflat quasi-Sasakian 5-manifolds. The most important results concerning Sasakian and cosymplectic manifolds reveal interesting relationships between the characteristics of these manifolds such as contact self-duality and constancy of the $\Phi$-holomorphic sectional curvature, contact anti-self-duality and Ricci flatness, etc.