Lie groups as four-dimensional special complex manifolds with Norden metric

TL;DR

This paper constructs a specific four-dimensional complex manifold with Norden metric using solvable Lie algebras, analyzes its curvature properties, and determines conditions for it to be isotropic Kählerian.

Contribution

It introduces a new family of four-dimensional special complex manifolds with Norden metric derived from solvable Lie algebras, including curvature analysis and isotropic Kählerian conditions.

Findings

Constructed a four-dimensional special complex manifold with constant holomorphic sectional curvature.

Analyzed the curvature properties of the manifold.

Provided necessary and sufficient conditions for the manifold to be isotropic Kählerian.

Abstract

An example of a four-dimensional special complex manifold with Norden metric of constant holomorphic sectional curvature is constructed via a two-parametric family of solvable Lie algebras. The curvature properties of the obtained manifold are studied. Necessary and sufficient conditions for the manifold to be isotropic K\"ahlerian are given.