Constructing a metallic semi-Riemannian manifold from an almost paracontact metric manifold

In this paper, we introduce a new method to obtain a metallic semi-Riemannian structure $(\mathrm{\Psi },\tilde{g})$ from the given almost paracontact metric structure $(\phi ,\xi ,\eta ,g)$ on a smooth manifold $M^{2n+1}$, and give the relations between these structures via Levi-Civita connections of $g$ and $\tilde{g}$. After, we discuss these relations for para-Kenmotsu and para-Sasakian structures and state the properties of obtained metallic semi-Riemannian structure. Furthermore, we show that metallic structures obtained from para-Kenmotsu and para-Sasakian structures are integrable and non-integrable, respectively. Also, we study the curvature properties of the obtained metallic structure and give explicit examples for the results of the study.