On the classification of almost contact metric manifolds

In this thesis, almost contact metric manifolds are examined in general terms. Firstly, some certain relations between the classes of almost contact metric manifolds and the almost Hermitian structures on the product of two almost contact metric manifolds are investigated and some new results are obtained. Secondly, the classes of almost contact metric structures, induced by the fundamental 3- forms of manifolds with $G_2$ structures, are studied and some results are gained by considering some certain properties of the characteristic vector fields of these structures. Furthermore, some examples about almost contact metric manifolds, induced by parallel and nearly-parallel $G_2$ structures, are given. In the final section, almost contact metric structures on five dimensional nilpotent Lie algebras studied. Also, left invariant almost contact metric structures on five dimensional nilpotent Lie groups are investigated by inquiring whether these structures are cosymplectic, nearly-cosymplectic, $\alpha$-Sasakian, $\beta$-Kenmotsu, almost-cosymplectic and semi-cosymplectic.