Almost (para-) contact metric $(κ,μ)$-manifolds. Part 1: Riemannian

Abstract

The author is planning if possible classify all three-dimensional $(κ,μ)$-manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic cases already is provdied. Up to authors knowledge there is no classification for para-contact or almost para-cosymplectic $(κ,μ)$. Conjecture is described by the author in coming paper structures provide classification. The main goal however is to show that these three dimensional manifolds are essentially building blocks of higher-dimensional manifolds. The other possiibilty is to introduce class of manifolds which contain both almost contact metric and almost para-contact metric manifolds as proper subclasses.