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Bifoliated homotopy invariant and metallic submersions. (English) Zbl 1476.53051

Summary: 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.

MSC:

53C12 Foliations (differential geometric aspects)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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