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

Martín-Molina Verónica (Universidad de Sevilla, Facultad de Ciencias de la Educación, Departamento de Didáctica de las Matemáticas, Sevilla, Spain)

We study paracontact metric (k,μ)-spaces with k = -1, equivalent to h2=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.

Keywords: paracontact metric manifold, (_, _)-spaces, paraSasakian, contact metric, nullity distribution