A quasi contact metric manifold is a natural generalization of a contact metric manifold based on the geometry of the corresponding quasi Kahler cones. In this paper we prove that if a quasi contact metric manifold has constant sectional curvature $c$, then $c=1$; additionally, if the characteristic vector field is Killing, then the manifold is Sasakian. These facts are some generalizations of Olszak's theorem to quasi contact metric manifolds.
"Quasi Contact Metric Manifolds with Constant Sectional Curvature." Tokyo J. Math. 41 (2) 515 - 525, December 2018. https://doi.org/10.3836/tjm/1502179276