Geometry of paraquaternionic contact structures

TL;DR

This paper introduces paraquaternionic contact structures as a generalization of para 3-Sasakian geometry, develops their fundamental properties, and identifies the flat model as the paraquaternionic Heisenberg group.

Contribution

It defines pqc structures, derives a preserving linear connection, and characterizes pqc-Einstein manifolds, linking them to para 3-Sasakian spaces and the paraquaternionic Heisenberg group.

Findings

Pqc structures generalize para 3-Sasakian geometry.

A distinguished linear connection with explicit torsion is constructed.

The paraquaternionic Heisenberg group is the flat model of pqc geometry.

Abstract

We introduce the notion of paraquaternionic contact structures (pqc structures), which turns out to be a generalization of the para 3-Sasakian geometry. We derive a distinguished linear connection preserving the pqc structure. Its torsion tensor is expressed explicitly in terms of the structure tensors and the structure equations of a pqc manifold are presented. We define pqc-Einstein manifolds and show that para 3-Sasakian spaces are precisely pqc manifolds, which are pqc-Einstein. Furthermore, we introduce the paraquaternionic Heisenberg qroup and show that it is the flat model of the pqc geometry.