Complex connections on conformal K\"ahler manifolds with Norden metric

TL;DR

This paper introduces a family of complex connections on conformal Kähler manifolds with Norden metric, analyzes their curvature tensors, and explores their conformal invariants and symmetry groups.

Contribution

It presents an eight-parameter family of complex connections on conformal Kähler Norden manifolds and derives their curvature tensors and conformal invariants.

Findings

Derived explicit form of curvature tensors for the connections.

Identified conformal invariants associated with these connections.

Analyzed the conformal group actions on the connections.

Abstract

An eight-parametric family of complex connections on a class complex manifolds with Norden metric is introduced. The form of the curvature tensor with respect to each of these connections is obtained. The conformal group of the considered connections is studied and some conformal invariants are obtained.