Einstein-Weyl structures on lightlike hypersurfaces

• Autorzy: Cyriaque Atindogbe , Lionel Bérard-Bergery , Carlos Ogouyandjou
• Języki publikacji: EN

Abstrakty

EN

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 ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.

Słowa kluczowe

EN

Lightlike hypersurface; Screen distribution; Einstein-Weyl structure

Kategorie tematyczne

• 53C05: Connections, general theory
• 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
• 53C50: Lorentz manifolds, manifolds with indefinite metrics

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1850-1862

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Cyriaque Atindogbe

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

autor

Lionel Bérard-Bergery

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

autor

Carlos Ogouyandjou

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

Bibliografia

• [1] Atindogbe C., Duggal K.L., Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math., 2004, 11(4), 421–442
• [2] Atindogbe C., Ezin J.-P., Tossa J., Pseudoinversion of degenerate metrics, Int. J. Math. Math. Sci., 2003, 55, 3479–3501 http://dx.doi.org/10.1155/S0161171203301309[Crossref]
• [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 http://dx.doi.org/10.1007/PL00001029[Crossref]
• [4] Duggal K.L., Bejancu A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Math. Appl., 364, Kluwer, Dordrecht, 1996 http://dx.doi.org/10.1007/978-94-017-2089-2[Crossref]
• [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
• [6] Ivanov S., Einstein-Weyl structures on compact conformal manifolds, Quart. J. Math. Oxford Ser., 1999, 50(200), 457–462 http://dx.doi.org/10.1093/qjmath/50.200.457[Crossref]
• [7] Kupeli D.N., Singular Semi-Riemannian Geometry, Math. Appl., 366, Kluwer, Dordrecht, 1996 http://dx.doi.org/10.1007/978-94-015-8761-7[Crossref]
• [8] LeBrun C., Mason L.J., The Einstein-Weyl equations, scattering maps, and holomorphic disks, Math. Res. Lett., 2009, 16(2), 291–301 [Crossref]
• [9] Pedersen H., Swann A., Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Proc. London Math. Soc., 1993, 66(2), 381–399 http://dx.doi.org/10.1112/plms/s3-66.2.381[Crossref]

Identyfikatory

DOI

10.2478/s11533-013-0278-9