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Twisted products in pseudo-Riemannian geometry

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Abstract

Twisted products are generalizations of warped products, namely the warping function may depend on the points of both factors. The two canonical foliations of a twisted product are mutually perpendicular and their leaves are totally geodesic, resp. totally umbilic. The main result is a decomposition theorem of de Rham type: If on a simply connected, geodesically complete pseudo-Riemannian manifoldM two foliations with the above properties are given, thenM is a twisted product.

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Authors and Affiliations

  1. Mathematisches Institut der Universität zu Köln, Weyertal 86-90, D-5000, Köln 41, Germany

    Ralf Ponge & Helmut Reckziegel

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  1. Ralf Ponge
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  2. Helmut Reckziegel
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Ponge, R., Reckziegel, H. Twisted products in pseudo-Riemannian geometry. Geom Dedicata 48, 15–25 (1993). https://doi.org/10.1007/BF01265674

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  • DOI: https://doi.org/10.1007/BF01265674

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