Almost (para-) contact metric \((\kappa,\mu)\)-manifolds. Part 1: Riemannian

The author is planning if possible classify all three-dimensional \((\kappa,\mu)\)-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...

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Bibliographic Details
Published inarXiv.org
Main Author Dacko, Piotr
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.06.2020
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Summary:The author is planning if possible classify all three-dimensional \((\kappa,\mu)\)-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 \((\kappa,\mu)\). 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.
ISSN:2331-8422