Quaternionic Kaehler manifolds with Hermitian and Norden metrics

TL;DR

This paper investigates quaternionic Kaehler manifolds equipped with Hermitian and Norden metrics, establishing conditions for isotropic hyper-Kaehlerian and flatness, and proving Einstein property for certain dimensions.

Contribution

It introduces new conditions for isotropic hyper-Kaehlerian and flatness, and characterizes Einstein quaternionic Kaehler manifolds with Hermitian and Norden metrics.

Findings

Manifolds are Einstein for dimension ≥ 8

Conditions for isotropic hyper-Kaehlerian and flatness are established

Classification of non-hyper-Kaehler quaternionic Kaehler manifolds

Abstract

Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kaehler manifolds are considered. Some necessary and sufficient conditions the investigated manifolds be isotropic hyper-Kaehlerian and flat are found. It is proved that the quaternionic Kaehler manifolds with the considered metric structure are Einstein for dimension at least 8. The class of the non-hyper-Kaehler quaternionic Kaehler manifold of the considered type is determined.