Almost complex connections on almost complex manifolds with Norden metric

TL;DR

This paper introduces a family of linear connections on almost complex manifolds with Norden metric, characterizes when they are natural, and explores their curvature properties on conformal Kähler manifolds.

Contribution

It defines new families of connections preserving the almost complex structure and analyzes their curvature, extending the understanding of geometric structures with Norden metrics.

Findings

Conditions for connections to be natural are established

Curvature tensors of certain complex connections are shown to coincide

New families of connections are characterized on specific manifolds

Abstract

A four-parametric family of linear connections preserving the almost complex structure is defined on an almost complex manifold with Norden metric. Necessary and sufficient conditions for these connections to be natural are obtained. A two-parametric family of complex connections is studied on a conformal K\"{a}hler manifold with Norden metric. The curvature tensors of these connections are proved to coincide.