Classification results for three-dimensional (para)contact metric and almost (para)cosymplectic $(\kappa,\mu)$-spaces

Abstract

It is provided an overview of existed results concerning classification of contact metric, almost cosymplectic and almost Kenmotsu $(\kappa,\mu)$-manifolds. In the case of dimension three it is described in full details structure of contact metric or almost cosymplectic $(\kappa,\mu)$-spaces. The second part of the paper addresses three-dimensional paracontact metric and almost paracosymplectic $(\kappa,\mu)$-spaces. There is obtained local classification of paracontact metric $(\kappa,\mu)$-spaces, and almost paracosymplectic $(\kappa,\mu)$-spaces, for every possible value of $\kappa$.