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arXiv · 1909.00797

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

Piotr Dacko
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Abstract

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.

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Piotr Dacko. 2019-09-02. Almost (para-) contact metric $(\kappa,\mu)$-manifolds. Part 1: Riemannian. https://arxiv.org/abs/1909.00797

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