Geodesic
On Geometric Analysis of the Dynamics of Volumetric Expansion and Its Applications to General Relativity
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 146 (2018), pp. 103-112
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In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its applications to the problem of the existence in the space-time of compact and complete spacelike hypersurfaces and to the global geometry of generalized Robertson–Walker space-times.
Keywords: volumetric expansion, vector field, flow, space-time, spacelike hypersurface. 
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S. E. Stepanov; I. E. Denezhkina; A. V. Ovchinnikov. On Geometric Analysis of the Dynamics of Volumetric Expansion and Its Applications to General Relativity. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 146 (2018), pp. 103-112. http://geodesic.mathdoc.fr/item/INTO_2018_146_a4/

[1] Arnold V. I., Khesin B. A., Topologicheskie metody v gidrodinamike, MTsNMO, M., 2007

[2] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya: metody i prilozheniya, Nauka, M., 1986

[3] Kobayasi Sh., Gruppy preobrazovanii v differentsialnoi geometrii, Nauka, M., 1986

[4] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, Nauka, M., 1981 | MR

[5] Mizner Ch., Torn K., Uiler Dzh., Gravitatsiya, Mir, M., 1977

[6] Penrouz R., Struktura prostranstva-vremeni, Mir, M., 1972

[7] Stepanov S. E., “Tekhnika Bokhnera dlya $m$-mernogo kompaktnogo mnogoobraziya s $\operatorname{SL}(m,\mathbb{R})$-strukturoi”, Algebra i analiz, 10:4 (1998), 192–209 | Zbl

[8] Stepanov S. E., “Ob odnom analiticheskom metode obschei teorii otnositelnosti”, Teor. mat. fiz., 122:3 (2000), 482–496 | DOI | MR | Zbl

[9] Alias L. J., Romero A., Sánchez M., “Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson–Walker spacetimes”, Gen. Relat. Grav., 27 (1995), 71–84 | DOI | MR | Zbl

[10] Beem J. K., Ehrlich P. E., Easley K. L., Global Lorentzian geometry, Marcel Dekker, New York, 1996 | MR | Zbl

[11] Caminha A., “The geometry of closed conformal vector fields on Riemannian spaces”, Bull. Braz. Math. Soc. New Ser., 42:2 (2011), 277–300 | DOI | MR | Zbl

[12] Caminha A., Souza P., Camargo F., “Complete foliations of space forms by hypersurfaces”, Bull. Braz. Math. Soc. New Ser., 41:3 (2010), 339–353 | DOI | MR | Zbl

[13] Costantino F., Thurston D., “3-Manifolds efficiently bound 4-manifolds”, J. Topol., 1:3 (2008), 703–745 | DOI | MR | Zbl

[14] Galloway G. J., “Some global aspects of compact space-times”, Arch. Math., 42:2 (1984), 168–172 | DOI | MR | Zbl

[15] Godinho L., Natario J., An introduction to Riemannian geometry with applications to mechanics and relativity, Springer-Verlag, Heidelberg–New York–London, 2014 | MR | Zbl

[16] Guillou L., Marin A., A la recherche de la topologie perdue, Birkhäuser, Boston–Basel–Stuttgart, 1986 | Zbl

[17] Gutierres M., Olea B., “Global decomposition of a Lorentzian manifold as a generalized Robertson–Walker space”, Differ. Geom. Appl., 27 (2009), 145–156 | MR

[18] Hawking S. W., Penrose R., “The singularities of gravitational collapse and cosmology”, Proc. Roy. Soc. A., 314 (1970), 529–548 | MR | Zbl

[19] Markus L., “Parallel dynamic systems”, Topology, 8 (1969), 47–57 | DOI | MR | Zbl

[20] O'Neil B., Semi-Riemannian geometry with applications to relativity, Academic Press, San Diego, 1983 | MR | Zbl

[21] Nishikawa S., “On maximal spacelike hypersurfaces in Lorentzian manifold”, Nagoya Math. J., 95 (1984), 117–124 | DOI | MR | Zbl

[22] Romero A., “The introduction of Bochner’s technique on Lorentzian manifolds”, Nonlin. Anal., 47:5 (2001), 3047–3059 | DOI | MR | Zbl

[23] Romero A., Rubio R. M., Salamanka J. J., “Uniqueness of complete maximal hypersurfaces in spatially parabolic generalized Robertson–Walker spacetimes”, Class. Quantum Grav., 30 (2013), 115007 | DOI | MR | Zbl

[24] Sachs R. K., Wu H., General relativity for mathematicians, Springer-Verlag, New York, 1977 | MR | Zbl

[25] Sánchez M., “On the geometry of generalized Robertson–Walker spacetimes: geodesics”, Gen. Relat. Grav., 30:6 (1998), 915–932 | DOI | MR

[26] Stepanov S. E., Mikeš J., “The generalized Landau–Raychaudhuri equation and its applications”, Int. J. Geom. Meth. Mod. Phys., 12:8 (2015), 1560026 | DOI | MR | Zbl

[27] Tu L. W., An introduction to manifolds, Springer, New York, 2008 | MR | Zbl

[28] Unal B., “Divergence theorems in semi-Riemannian geometry”, Acta Appl. Math., 40 (1995), 173–178 | DOI | MR | Zbl