A General Type of Almost Contact Manifolds

Among almost contact manifolds Sasakian manifolds, Kenmotsu manifolds (called also “a certain class of almost contact manifolds”) and cosymplectic manifolds have been studied by many authors. The purpose of this paper is to obtain a class of almost contact manifolds which will generalize the above manifolds. The paper generalizes the RK-manifolds introduced by Lieven Vanhecke. I give some results concerning the submanifolds of these spaces, the behaviour of these submanifolds at conformal, projective and concircular transformations. Also I obtain a similar result with those on RK-manifolds but in a form a little weaker when they satisfy the axiom of 2p+1-coholomorphic spheres.