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

Abstract

We study paracontact metric $(\kappa ,\mu )$-spaces with $\kappa =-1$, 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 $(-1,\mu )$-spaces with tensor $h$ of non-constant rank, which were not known to exist until now.

9 pages

References in corpus (2)

• Nullity conditions in paracontact geometry
• Non-existence of flat paracontact metric structures in dimension greater than or equal to five

Cited by in corpus (1)

• On a remarkable class of paracontact metric manifolds