MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.18, sa.4, 2021 (SCI-Expanded)
In this paper, we prove that the signature of a compact oriented Riemannian manifold supporting two orthogonal Riemannian foliations is a bifoliated homotopy invariant. We apply this result on locally decomposable metallic Riemannian manifolds. We also introduce the notion of metallic submersions between two metallic Riemannian manifolds and we study some of its properties and give an example.