Abstract:
In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermition almost contact metric spaces, is introduced.
Key words:almost contact manifold, Sasakian manifold, $K$-contact manifold, the intrinsic geometry of almost contact metric manifolds.