ABOUT AP-MANIFOLD STRUCTURE ON CODISTRIBUTION SASAKI MANIFOLD

The article introduces the concept of AP-manifold which is a special case of the SQS-diversity. On codistribution D* contact metric structure of (M, ⃗ξ, η, φ, g, D) is determined by the extended almost contact metric structure of (D, ⃗u = ∂n, μ = ηˆ π*, J, G, D̃). $ It is proved that the extended structure is the SQS-structure if and only if the original manifold as selected Sasaki manifold with zero curvature distribution.