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

Abstract

In this paper, we introduce a new method to obtain a metallic semi-Riemannian structure (Ψ,g) from the given almost paracontact metric structure (φ,ξ,η,g) on a smooth manifold M2n+1, and give the relations between these structures via Levi-Civita connections of g and 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.