Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
Null hypersurfaces; null rigging; Newton transformations; Minkowski integral formulas.
Null hypersurfaces; null rigging; Newton transformations; Minkowski integral formulas.
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.
References:
[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, DOI 10.1017/S0013091502000500 | MR 1998575
[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, DOI 10.1017/S1474748006000077 | MR 2261223 | Zbl 1118.53038
[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, DOI 10.1007/BF02105675 | MR 1310212
[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, DOI 10.2748/tmj/1178225107 | MR 1464181 | Zbl 0912.53046
[5] Atindogbe, C.: Blaschke type normalization on light-Like Hypersurfaces. Journal of Mathematical Physics, Analysis, Geometry, 6, 4, 2010, 362-382, MR 2789299 | Zbl 1230.53013
[6] Atindogbe, C.: Normalization and prescribed extrinsic scalar curvature on null hypersurfaces. Journal of Geometry and Physics, 60, 2010, 1762-1770, DOI 10.1016/j.geomphys.2010.06.018 | MR 2679419
[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
[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
[9] Atindogbe, C., Ezin, J.-P., Tossa, J.: Pseudo-inversion of degenerate metrics. Int. J. of Mathematics and Mathematical Sciences, 55, 2003, 3479-3501, DOI 10.1155/S0161171203301309 | MR 2019290
[10] Bivens, I.: Integral formulas and hyperspheres in a simply connected space form. Proc.Am. Math. Soc., 88, 1983, 113-118, DOI 10.1090/S0002-9939-1983-0691289-2 | MR 0691289 | Zbl 0523.53053
[11] Dong, J., Liu, X.: Totally Umbilical Lightlike Hypersurfaces in Robertson-Walker Spacetimes. ISRN Geometry, 2014, 2014, Article ID 974695, http://dx.doi.org/10.1155/2014/974695. DOI 10.1155/2014/974695. | MR 3187030 | Zbl 1293.53019
[12] Duggal, K. L., Bejancu, A.: Degenerate hypersurface of semi-Riemannian manifolds. Bull. Inst. Politehnie Iasi (S.1), 37, 1991, 13-22, MR 1313822
[13] Duggal, K. L., Giménez, A.: Lightlike hypersurfaces of Lorentzian manifolds with distinguished screen. Journal of Geometry and Physics, 55, 2005, 107-122, DOI 10.1016/j.geomphys.2004.12.004 | MR 2157417 | Zbl 1111.53029
[14] Gutierrez, M., Olea, B.: Lightlike hypersurfaces in Lorentzian manifolds. arXiv: 1207.1030v1 [math.DG], 2012,
[15] Hsiung, C. C.: Some integral formulas for closed hypersurfaces. Math. Scand., 2, 1954, 286-294, DOI 10.7146/math.scand.a-10415 | MR 0068236
[16] Mars, M., Wolf, T.: $G_{2}$ perfect-fluid cosmologies with a proper conformal Killing vector. Class. Quantum Grav., 14 2303, 1997, DOI 10.1088/0264-9381/14/8/026 | MR 1468585
Search
Partner of
