Remarks on metallic warped product manifolds

TL;DR

This paper investigates metallic structures on warped product manifolds, providing characterizations, conditions for local metallicity, and concrete examples to advance understanding of metallic geometry.

Contribution

It offers a new characterization of metallic structures on product manifolds and establishes conditions for warped products to be locally metallic, including explicit examples.

Findings

Characterization of metallic structures via metallic maps

Necessary and sufficient conditions for warped products to be locally metallic

An example of a metallic warped product Riemannian manifold

Abstract

We characterize the metallic structure on the product of two metallic manifolds in terms of metallic maps and provide a necessary and sufficient condition for the warped product of two locally metallic Riemannian manifolds to be locally metallic. The particular case of product manifolds is discussed and an example of metallic warped product Riemannian manifold is provided.