Exploring certain geometric and harmonic properties of the Berger-type metric conformal deformation on the Para-K\"ahler-Norden manifold

TL;DR

This paper investigates a new class of conformally deformed Berger-type metrics on para-K"ahler-Norden manifolds, analyzing their curvature properties and harmonic maps to understand their geometric structure.

Contribution

It introduces a novel conformal deformation of Berger-type metrics on para-K"ahler-Norden manifolds and explores their curvature and harmonic map properties.

Findings

Derived the Levi-Civita connection for the new metrics

Classified the curvature varieties of the deformed metrics

Analyzed harmonic maps within this geometric framework

Abstract

This work presents a novel class of metrics on a para-K\"{a}hler-Norden manifold $(M^{2m},F,g)$, derived from a conformal deformation of the Berger-type metric associated with the metric $g$. Initially, we examine the Levi-Civita link associated with this metric. Secondly, we delineate all varieties of curvature for a manifold $M$ equipped with a conformal deformation of Berger-type metric for $g$. Finally, we studied a certain class of harmonic maps.