Some Four-dimensional Almost Hypercomplex Pseudo-hermitian Manifolds

In the study of almost hypercomplex manifolds the Hermitian metrics are well known. The parallel study of almost hypercomplex manifolds with skewHermitian metrics is in progress of development 6, 7. Let (M,H) be an almost hypercomplex manifold, i.e. M is a 4n-dimensional differentiable manifold and H is a triple (J1, J2, J3) of anticommuting almost complex structures, where J3 = J1 ◦ J2 8,2. A standard hypercomplex structure for all x(x, y, u, v) ∈ TpM , p ∈ M is defined in 8 as follows J1x(−y, x, v,−u), J2x(−u,−v, x, y), J3x(v,−u, y,−x). (1)