Among almost contact manifolds Sasakian manifolds, Kenmotsu manifolds (called also "a certain class of almost contact manifolds") andcosymplectic manifolds have been studied by many authors. The purpose of this paper is to obtain a class of almost contact manifolds which willgeneralize the above manifolds. The paper generalizes the RK-manifolds introduced by Lieven Vanhecke. I give some results concerning thesubmanifolds of these spaces, the behaviour of these submanifolds at conformal,

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... ve and concircular transformations. Also I obtain a similarresult with those on RK-manifolds but in a form a little weaker when they satisfy the axiom of 2p+1-coholomorphic spheres.