distribution of zero curvature

Extended Structures on Codistributions of Contact Metric Manifolds

Authors: Galaev S. V.

In the paper, the notion of an AP-manifold is introduced. Such a manifold is an almost contact metric manifold that is locally equivalent to the direct product of a contact metric manifold and an 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 K¨ ahlerian manifold.

Admissible Hypercomplex Structures on Distributions of Sasakian Manifolds

Authors: Galaev S. V.

The notions of admissible (almost) hypercomplex structure and almost contact hyper-Kahlerian structure are introduced. On a ¨ manifold M with an almost contact metric structure (M, ~ξ, η, ϕ, D) an interior symmetric connection ∇ is defined. In the case of a contact manifold of dimension bigger than or equal to five, it is proved that the curvature tensor of the connection ∇ is zero if and only if there exist adapted coordinate charts with respect to that the coefficients of the interior connection are zero.