Canonical connection on quasi-Kaehler manifolds with Norden metric

TL;DR

This paper investigates the properties of the canonical connection on quasi-Kaehler manifolds with Norden metric, focusing on curvature, torsion, and their relations to other geometric connections.

Contribution

It provides new conditions for isotropic-Kaehler manifolds and explores the relationships between different connections on these manifolds.

Findings

Canonical connection with Kaehler curvature tensor characterized.

Conditions for parallel torsion in the canonical connection derived.

Relations between canonical, B-, and skew-symmetric torsion connections established.

Abstract

We study the geometry of the canonical connection on a quasi-Kaehler manifold with Norden metric. We consider the cases when the canonical connection has Kaehler curvature tensor and parallel torsion, and derive conditions for an isotropic-Kaehler manifold. We give the relation between the canonical connection, the B-connection, and the connection with totally skew-symmetric torsion on quasi-Kaehler manifolds with Norden metric.