English

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

Differential Geometry 2020-09-23 v2

Abstract

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

Keywords

Cite

@article{arxiv.2009.00372,
  title  = {Classification results for three-dimensional (para)contact metric and almost (para)cosymplectic $(\kappa,\mu)$-spaces},
  author = {Piotr Dacko},
  journal= {arXiv preprint arXiv:2009.00372},
  year   = {2020}
}

Comments

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 $\kappa$