Generalized metallic structures

TL;DR

This paper explores generalized metallic structures on manifolds, examining their properties, integrability conditions, and how they can be lifted to tangent and cotangent bundles using generalized geometry techniques.

Contribution

It introduces new generalized metallic, product, and complex structures induced by metallic Riemannian structures and studies their integrability and relations on different bundles.

Findings

Conditions for integrability of generalized metallic structures

Lifting metallic structures to tangent and cotangent bundles

Relations between structures on different bundles

Abstract

We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of $M$ by a metallic Riemannian structure $(J,g)$ on $M$, providing conditions for their integrability with respect to a suitable connection. Moreover, by using methods of generalized geometry, we lift $(J,g)$ to metallic Riemannian structures on the tangent and cotangent bundles of $M$, underlying the relations between them.