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arXiv · 1408.6784

Local classification and examples of an important class of paracontact metric manifolds

Verónica Martín-Molina
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Abstract

We study paracontact metric $(κ,μ)$-spaces with $κ=-1$, equivalent to $h^2=0$ but not $h=0$. In particular, we will give an alternative proof of Theorem 3.2 of [11] and present examples of paracontact metric $(-1,2)$-spaces and $(-1,0)$-spaces of arbitrary dimension with tensor $h$ of every possible constant rank. We will also show explicit examples of paracontact metric $(-1, μ)$-spaces with tensor $h$ of non-constant rank, which were not known to exist until now.

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Verónica Martín-Molina. 2014-08-28. Local classification and examples of an important class of paracontact metric manifolds. https://doi.org/10.2298/fil1503507m

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