почти контактная метрическая структура

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.

Almost Contact Metric Spaces with N-connection

Authors: Galaev S. V.

On a manifold with an almost contact metric structure (ϕ, ~ξ, η, g,X,D) and an endomorphism N : D → D, a notion of the N-connection is introduced. The conditions under which an N-connection is compatible with an almost contact metric structure ∇Nη = ∇Ng = ∇N~ξ = 0 are found. The relations between the Levi – Civita connection, the Schouten – van-Kampen connection and the N-connection are investigated. Using the N-connection the conditions under which an almost contact metric structure is an almost contact Kahlerian structure are investigated.

Almost Contact Metric Structures Defined by a Symplectic Structure Over a Distribution

Authors: Galaev S. V., Shevzova Y. V.

The distribution D of an almost contact metric structure (ϕ, ξ, η, g) is an odd analogue of the tangent bundle. In the paper an intrinsic symplectic structure naturally associated with the initial almost contact metric structure is constructed. The interior connection defines the parallel transport of admissible vectors (i.e. vectors belonging to the distribution D) along admissible curves. Each corresponding extended connection is a connection in the vector bundle (D, π,X) defined by the interior connection and by an endomorphism N : D → D.