A Lie group as a 4-dimensional quasi-Kaehler manifold with Norden metric

TL;DR

This paper constructs a 4-dimensional quasi-Kaehler manifold with Norden metric on a Lie group, characterizes its geometry, and determines conditions for it to be isotropic Kaehler.

Contribution

It introduces a 4-parametric family of quasi-Kaehler manifolds with Norden metric on Lie groups and provides geometric characterization and conditions for isotropic Kaehlerity.

Findings

Explicit 4-parametric family constructed

Geometric characterization provided

Condition for isotropic Kaehlerity derived

Abstract

A 4-parametric family of 4-dimensional quasi-Kaehler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically. The condition for such a 4-manifold to be isotropic Kaehler is given.