Some Results On (K,?)'-almost Kenmotsu Manifolds

In this paper,we introduce the basic concepts of almost contact metric manifolds,and mainly study the local structure theorem of a special almost Kenmotsu manifold——(k,?)'-almost Kenmotsu manifold.Firstly,the definition of(k,?)'-almost Kenmotsu manifold is introduced.Some properties of(k,?)'-almost Kenmotsu manifold are given.In this paper,we study the quasi-conformal curvature tensor C and projective curvature tensor P on a(k,?)'-almost Kenmotsu manifold M2n+1 of dimension greater than 3.We obtain that if M2n+1 is non-Kenmotsu and satisfies R(X,Y)·C=0 or P(X,Y)·P=0,then it is locally isometric to the Riemannian product Hn+1(-4)×Rn.