Generalized Kenmotsu manifold constancy of type

In this work we consider generalized Kenmotsu manifolds, we introduce: the fourth and the fifth fundamental identities of generalized Kenmotsu manifolds; the first and the second structural tensors of generalized Kenmotsu manifolds (and we prove their properties); the concept of adjoint Q-algebra for generalized Kenmotsu manifolds. We prove that generalized Kenmotsu manifolds and the II kind special generalized Kenmotsu manifolds have anticommutative adjoint Q-algebra. And the Kenmotsu manifolds and the I kind special generalized Kenmotsu manifolds have Abelian adjoint Q-algebra. The type constancy contact analog is introduced and the constant-type generalized Kenmotsu manifolds are thoroughly examined. We have identified the type point constancy conditions of the generalized Kenmotsu manifolds in the adjoint G-structure space. We prove that the zero constant type GK-manifold class coincides with the Kenmotsu manifold class and the non-zero constant type GK-manifold class can be concircularly transformed into the almost contact metric manifolds locally equivalent to the product of the six dimensional NK-eigenmanifold and the real straight line.