Quasi-Kaehler manifolds with a pair of Norden metrics

TL;DR

This paper studies a specific class of non-integrable almost complex manifolds equipped with two Norden metrics, exploring their geometric properties and characterizing a family of 4-dimensional quasi-Kaehler manifolds with respect to their Levi-Civita connection.

Contribution

It introduces a 4-parameter family of 4-dimensional quasi-Kaehler manifolds with Norden metrics and analyzes their properties related to Levi-Civita connections.

Findings

Characterization of a 4-parameter family of quasi-Kaehler manifolds

Relations between geometric quantities under connection transformations

Insights into non-integrable almost complex structures with Norden metrics

Abstract

The basic class of the non-integrable almost complex manifolds with a pair of Norden metrics are considered. The interconnections between corresponding quantities at the transformation between the two Levi-Civita connections are given. A 4-parametric family of 4-dimensional quasi-Kaehler manifolds with Norden metric is characterized with respect to the associated Levi-Civita connection.