On almost cosymplectic manifolds

Abstract

On such manifold we may always define a 2-form Φ by Φ(X, Y)~g(φX, Y). (Λf, φ, ξ, 7], g) is said to be an almost cosymplectic manifold (cf.[2]) if the forms Φ and Ύ] are closed, i.e. dΦ=0 and dη^O, where d is the operator of exterior differentiation.In particular, if the almost contact structure of an almost cosymplectic manifold is normal, then it is said to be a cosymplectic manifold (cf.[1]).