Locally warped products arising from certain group actions

Lappas, Dionyssios

doi:10.4099/math1924.20.365

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Isometric Actions Of Lie Groups1

Introduction1

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2011

2012

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Cited by 2 publications

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References 8 publications

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“…The following statement may be used to settle a warped product structure in many situations. It unifies and generalizes most of the existing results on the subject (see for instance [7,11,13,16,17,22]).…”

Section: Isometric Actions Of Lie Groupssupporting

confidence: 80%

Geometry of warped products

Zeghib

2011

Preprint

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This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we have interpreted statements, especially by means of a physical terminology. This is essentially heuristic, but we think it might be helpful in both directions, that is, in going from a synthetic geometrical language to a relativistic one, and vice-versa.

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Section: Isometric Actions Of Lie Groupssupporting

confidence: 80%

Geometry of warped products

Zeghib

2011

Preprint

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“…Doubly warped and warped structures appear in different situations. For example, Codazzi tensors with exactly two eigenvalues, one of them constant [5], Killing tensors [9], semi-Riemann submersions with umbilic fibres and some additional hypotheses [8] and certain group actions [1,16] lead to (doubly) warped structures. On the other hand, the translation of physical content into geometrical language gives rise to warped structures which, by a topological simplification, are supposed global products.…”

Section: Introductionmentioning

confidence: 99%

Semi-Riemannian manifolds with a doubly warped structure

Gutiérrez¹,

Olea²

2012

Rev. Mat. Iberoam.

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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.2000 Mathematics Subject Classification. Primary 53C50, Secondary 53C12.

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Locally warped products arising from certain group actions

Cited by 2 publications

References 8 publications

Geometry of warped products

Geometry of warped products

Semi-Riemannian manifolds with a doubly warped structure

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