Revista Matemática Iberoamericana

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Volume 28, Issue 1, 2012, pp. 1–24
DOI: 10.4171/RMI/664

Published online: 2012-01-20

Semi-Riemannian manifolds with a doubly warped structure

Manuel Gutiérrez[1] and Benjamín Olea[2]

(1) Universidad de Málaga, Spain
(2) Universidad de Málaga, Spain

We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly warped product up to a zero measure subset formed by an union of leaves. We also obtain a necessary and sufficient condition which ensures the decomposition of the whole manifold and use it to give sufficient conditions of geometrical nature. Finally, we study the uniqueness of direct product decomposition in the nonsimply connected case.

Keywords: Quotient manifold, doubly warped product, doubly warped structure, decomposition theorems

Gutiérrez Manuel, Olea Benjamín: Semi-Riemannian manifolds with a doubly warped structure. Rev. Mat. Iberoamericana 28 (2012), 1-24. doi: 10.4171/RMI/664