Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such structure

TL;DR

This paper explores almost hypercomplex pseudo-Hermitian manifolds, introduces isotropic hyper-K"ahler manifolds, and constructs a 4-parameter family of such manifolds on a Lie group, providing geometric characterization and conditions for isotropic hyper-K"ahlerity.

Contribution

It introduces the concept of isotropic hyper-K"ahler manifolds and constructs a new 4-parameter family of these manifolds on a Lie group, with geometric characterization.

Findings

A 4-parameter family of 4-dimensional manifolds is constructed.

Conditions for a manifold to be isotropic hyper-K"ahler are established.

Geometric characterization of the constructed family is provided.

Abstract

Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-K\"ahler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized geometrically. The condition a 4-manifold to be isotropic hyper-K\"ahler is given.