Almost contact metric and metallic Riemannian structures

Abstract

The metallic structure is a fascinating topic that continually generates new ideas. In this work, new metallic manifolds are constructed starting from both almost contact metric manifolds and we obtain some important notions like the metallic deformation. We show that there exists a correspondence between the metallic Riemannian structures and the almost contact metric structures. We give an open question where we propose the first step to study the reverse, i.e. the construction of an almost contact metric structure starting from a metallic Riemannian structure. We give a concrete example to confirm this construction.