Semi-Riemannian manifolds with a doubly warped structure

Details Semi-Riemannian manifolds with a doubly warped structure Semi-Riemannian manifolds with a doubly warped structure

2009-05-29

arxiv.org/abs/0905.4919v1

Mathematics

Differential Geometry

22 pages

Scientific paper

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 non simply connected case.

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