INFINITESIMAL TRANSFORMATIONS OF PROLONGED ALMOST CONTACT STRUCTURE WITH SASAKI METRIC

Almost contact metric structure is determined on distribution D of manifold M with an almost contact metric structure of (M, ξ , η, φ, g, D) using associated connection. It called extended almost contact metric structure with Sasaki metric. We study the infinitesimal transformations of obtained structure. Conditions are found under which the vector field defined on the distribution of almost contact metric structure keeps the extended structure.