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 $\kappa$.

4 tables. arXiv admin note: text overlap with arXiv:1909.00797. Local classification for paracontact metric and paracosymplectic manifolds extended for all possible value of $\kappa$