On a remarkable class of paracontact metric manifolds

TL;DR

This paper investigates a unique class of paracontact metric manifolds without contact metric equivalents, providing explicit examples with various ranks of a specific tensor, expanding understanding of their structure.

Contribution

It introduces and constructs explicit examples of paracontact metric (-1,μ)-spaces that are not paraSasakian, including cases with constant and non-constant rank of the tensor.

Findings

Existence of paracontact (-1,μ)-spaces not paraSasakian.

Explicit examples with all possible constant ranks of the tensor.

New examples with non-constant rank tensor.

Abstract

We study a remarkable class of paracontact metric manifolds which have no contact metric counterpart: the paracontact metric $(-1,\widetilde\mu)$-spaces which are not paraSasakian (i.e. have $\widetilde h\neq0$). We present explicit examples with $\widetilde h$ of every possible constant rank and some with non-constant rank, which were not known to exist until recently.