Geodesics and $F$-geodesics on tangent bundle with $\varphi$-Sasaki metric over para-K\"{a}hler-Norden manifold

TL;DR

This paper studies geodesics and $F$-geodesics on tangent bundles with a special metric over para-Kähler-Norden manifolds, expanding understanding of geometric structures in differential geometry.

Contribution

It introduces analysis of geodesics and $F$-geodesics on tangent and $ ext{phi}$-unit tangent bundles with the $ ext{phi}$-Sasaki metric over para-Kähler-Norden manifolds, a novel geometric setting.

Findings

Characterization of geodesics on tangent bundles with $ ext{phi}$-Sasaki metric.

Analysis of $F$-geodesics in the context of para-Kähler-Norden manifolds.

Insights into the geometric structure of tangent bundles over para-Kähler-Norden manifolds.

Abstract

In this paper, we investigate some geodesics and $F$-geodesics problems on tangent bundle and on $\varphi$-unit tangent bundle $T^{\varphi}_{1}M$ equipped with the $\varphi$-Sasaki metric over para-K\"{a}hler-Norden manifold $(M^{2m}, \varphi, g)$.