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Einstein-Weyl structures on lightlike hypersurfaces

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Central European Journal of Mathematics

Abstract

We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ n+21 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.

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References

  1. Atindogbe C., Duggal K.L., Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math., 2004, 11(4), 421–442

    MathSciNet  MATH  Google Scholar 

  2. Atindogbe C., Ezin J.-P., Tossa J., Pseudoinversion of degenerate metrics, Int. J. Math. Math. Sci., 2003, 55, 3479–3501

    Article  MathSciNet  Google Scholar 

  3. Chrusciel P.T., Delay E., Galloway G.J., Howard R., Regularity of horizons and the area theorem, Ann. Henri Poincaré, 2001, 2(1), 109–178

    Article  MathSciNet  MATH  Google Scholar 

  4. Duggal K.L., Bejancu A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Math. Appl., 364, Kluwer, Dordrecht, 1996

    Book  MATH  Google Scholar 

  5. Gauduchon P., Structures de Weyl-Einstein, espaces de twisteurs et variétés de type S 1×S 3, J. Reine Angew. Math., 1995, 469, 1–50

    MathSciNet  MATH  Google Scholar 

  6. Ivanov S., Einstein-Weyl structures on compact conformal manifolds, Quart. J. Math. Oxford Ser., 1999, 50(200), 457–462

    Article  MathSciNet  MATH  Google Scholar 

  7. Kupeli D.N., Singular Semi-Riemannian Geometry, Math. Appl., 366, Kluwer, Dordrecht, 1996

    Book  MATH  Google Scholar 

  8. LeBrun C., Mason L.J., The Einstein-Weyl equations, scattering maps, and holomorphic disks, Math. Res. Lett., 2009, 16(2), 291–301

    MathSciNet  MATH  Google Scholar 

  9. Pedersen H., Swann A., Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Proc. London Math. Soc., 1993, 66(2), 381–399

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut de Mathematiques et de Sciences Physiques, Université d’Abomey-Calavi, Benin, 01, BP 613, Porto-Novo, Benin

    Cyriaque Atindogbe & Carlos Ogouyandjou

  2. Institut Elie Cartan, Université Henri Poincaré, Nancy I, B.P. 239 54506, Vandœuvre-lès Nancy Cedex, France

    Lionel Bérard-Bergery

Authors
  1. Cyriaque Atindogbe
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  2. Lionel Bérard-Bergery
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  3. Carlos Ogouyandjou
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Correspondence to Cyriaque Atindogbe.

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Atindogbe, C., Bérard-Bergery, L. & Ogouyandjou, C. Einstein-Weyl structures on lightlike hypersurfaces. centr.eur.j.math. 11, 1850–1862 (2013). https://doi.org/10.2478/s11533-013-0278-9

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  • DOI: https://doi.org/10.2478/s11533-013-0278-9

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