Some results on geodesics and $F$-geodesics in tangent bundle with $\varphi$-Sasakian metric over para-K\"{a}hler-Norden manifold

Abstract

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