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Title: Newton transformations on null hypersurfaces (English)
Author: Fotsing, Cyriaque Atindogbé and Hans Tetsing
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 23
Issue: 1
Year: 2015
Pages: 57-83
Summary lang: English
Category: math
Summary: Any rigged null hypersurface is provided with two shape operators: with respect to the rigging and the rigged vector fields respectively. The present paper deals with the Newton transformations built on both of them and establishes related curvature properties. The laters are used to derive necessary and sufficient conditions for higher-order umbilicity and maximality we introduced in passing, and develop general Minkowski-type formulas for the null hypersurface, supported by some physical models in perfect-fluid space-times. (English)
Keyword: Null hypersurfaces
Keyword: null rigging
Keyword: Newton transformations
Keyword: Minkowski integral formulas.
MSC: 53B30
MSC: 53C42
MSC: 53Z05
idZBL: Zbl 1342.53028
idMR: MR3394078
Date available: 2015-08-25T14:00:12Z
Last updated: 2018-01-10
Stable URL:
Reference: [1] Alías, L. J., Jr, A. Brasil, Colares, A. Gervasio: Integral formulas for spacelike hypersurfaces in conformally stationary space-times and applications.Proc. Edinb. Math. Soc., 46, 2003, 465-488, MR 1998575, 10.1017/S0013091502000500
Reference: [2] Alías, L. J., Lira, J. H. S. de, Malacarne, J. M.: Constant higher-order mean curvature hypersurfaces in Riemannian spaces.Journal of the Institute of Mathematics of Jussieu, 5, 04, 2006, 527-562, Zbl 1118.53038, MR 2261223, 10.1017/S1474748006000077
Reference: [3] Alías, L. J., Romero, A., Sánchez, M.: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in Generalized Robertson-Walker space-times.Gen. Relat. Grav., 27, 1995, 71-84, MR 1310212, 10.1007/BF02105675
Reference: [4] Alías, L. J., Romero, A., Sánchez, M.: Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems.Tohoku Math. J., 49, 1997, 337-345, Zbl 0912.53046, MR 1464181, 10.2748/tmj/1178225107
Reference: [5] Atindogbe, C.: Blaschke type normalization on light-Like Hypersurfaces.Journal of Mathematical Physics, Analysis, Geometry, 6, 4, 2010, 362-382, Zbl 1230.53013, MR 2789299
Reference: [6] Atindogbe, C.: Normalization and prescribed extrinsic scalar curvature on null hypersurfaces.Journal of Geometry and Physics, 60, 2010, 1762-1770, MR 2679419, 10.1016/j.geomphys.2010.06.018
Reference: [7] Atindogbe, C., Berard-Bergery, L.: Distinguished normalization on non-minimal null hypersurfaces.Mathematical Sciences and Applications E-notes, 1, 1, 2013, 18-35, Zbl 1353.53070
Reference: [8] Atindogbe, C., Duggal, K.L.: Conformal screen on null hypersurfaces.Int. J. of Pure and Applied Math., 11, 4, 2004, 421-442, MR 2039644
Reference: [9] Atindogbe, C., Ezin, J.-P., Tossa, J.: Pseudo-inversion of degenerate metrics.Int. J. of Mathematics and Mathematical Sciences, 55, 2003, 3479-3501, MR 2019290, 10.1155/S0161171203301309
Reference: [10] Bivens, I.: Integral formulas and hyperspheres in a simply connected space form.Proc.Am. Math. Soc., 88, 1983, 113-118, Zbl 0523.53053, MR 0691289, 10.1090/S0002-9939-1983-0691289-2
Reference: [11] Dong, J., Liu, X.: Totally Umbilical Lightlike Hypersurfaces in Robertson-Walker Spacetimes.ISRN Geometry, 2014, 2014, Article ID 974695, Zbl 1293.53019, MR 3187030, 10.1155/2014/974695.
Reference: [12] Duggal, K. L., Bejancu, A.: Degenerate hypersurface of semi-Riemannian manifolds.Bull. Inst. Politehnie Iasi (S.1), 37, 1991, 13-22, MR 1313822
Reference: [13] Duggal, K. L., Giménez, A.: Lightlike hypersurfaces of Lorentzian manifolds with distinguished screen.Journal of Geometry and Physics, 55, 2005, 107-122, Zbl 1111.53029, MR 2157417, 10.1016/j.geomphys.2004.12.004
Reference: [14] Gutierrez, M., Olea, B.: Lightlike hypersurfaces in Lorentzian manifolds.arXiv: 1207.1030v1 [math.DG], 2012,
Reference: [15] Hsiung, C. C.: Some integral formulas for closed hypersurfaces.Math. Scand., 2, 1954, 286-294, MR 0068236, 10.7146/math.scand.a-10415
Reference: [16] Mars, M., Wolf, T.: $G_{2}$ perfect-fluid cosmologies with a proper conformal Killing vector.Class. Quantum Grav., 14 2303, 1997, MR 1468585, 10.1088/0264-9381/14/8/026


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