Novel theorems for the cotangent bundle endowed with metallic structures on a differentiable manifold.

The present paper aims to study the complete, horizontal and diagonal lifts of metallic structures in the cotangent bundle. Furthermore, the Nijenhuis tensor of a metallic structure is calculated and its integrability conditions by means of partial differential equations are established.

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons.

In this article, we examine gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in generalized Robertson-Walker (GRW) spacetimes. Besides, we demonstrate that in this scenario the GRW spacetime presents the Robertson-Walker (RW) spacetime and the perfect fluid (PF) spacetime presents the phantom era. Consequently, we show that if a GRW spacetime permits a gradient τ-Einstein solitons, then it also represents a PF spacetime under certain condition.