On hypercomplex pseudo-Hermitian manifolds

TL;DR

This paper studies hypercomplex pseudo-Hermitian manifolds, proving their flatness under certain conditions, exploring conformal transformations, and analyzing their invariance and equivalence classes.

Contribution

It introduces conformal transformations for these manifolds and characterizes their invariance and equivalence, extending understanding of their geometric properties.

Findings

Manifolds with 3 parallel complex structures are flat.

Conformal transformations preserve key properties of these manifolds.

A known example is characterized in relation to the results.

Abstract

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal invariance and the conformal equivalence of the basic types manifolds are studied. A known example is characterized in relation to the obtained results.