Admissible Hyper-Complex Pseudo-Hermitian Structures

Abstract

The notions of an admissible pseudo-Kählerian structure and of an admissible hypercomplex pseudo-Hermitian structure are introduced. On the distribution D of an almost contact structure (M, \(\vec \xi \), η, φ, g, D) with a Norden metric, using a prolonged connection ∇^N, an admissible almost hyper-complex pseudo-Hermitian structure (\(D,{J_1},{J_2},{J_3},\vec u,\lambda = \eta \circ {\pi _*},\tilde g,\tilde D\)) is defined. It is shown that if the initial almost contact structure with a Norden metric is an admissible pseudo- Kählerian structure with zero Schouten curvature tensor, then the induced admissible almost hypercomplex pseudo-Hermitian structure on the distribution D is integrable.