GEOMETRY OF SQS-MANIFOLDS

In the paper, the notion of an almost AP-manifold is introduced. Such a manifold is an almost contact metric manifold with an almost product structure of a special form. An almost AP-manifold with an integrable almost product structure is called in the paper an AP-manifold. An AP-manifold is locally equivalent to the direct product of a contact metric manifold and an almost Hermitian manifold. A normal AP-manifold with a closed fundamental form is a quasi-Sasakian manifold. A quasi-Sasakian AP-manifold is called in the paper a special quasi-Sasakian manifold (SQS-manifold). A SQS-manifold is locally equivalent to the product of a Sasakian manifold and a Kählerian manifold. The structure of the Schouten tensor of a SQS-manifold is studied. The conditions for a SQS-manifold to be an $eta$-Einstein manifold are studied.