Classification results for three-dimensional (para)contact metric and almost (para)cosymplectic (κ,μ)(κ,μ)-spaces

preprint2020arXivOpen access

Abstract

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

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