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2014 | 12 | 10 | 1586-1601
Tytuł artykułu

Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all rotational quasi-minimal surfaces of elliptic, hyperbolic and parabolic type, respectively.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
10
Strony
1586-1601
Opis fizyczny
Daty
wydano
2014-10-01
online
2014-06-21
Twórcy
Bibliografia
  • [1] Chen, B.-Y., Classification of marginally trapped Lorentzian flat surfaces in \(\mathbb{E}_2^4 \) and its application to biharmonic surfaces, J. Math. Anal. Appl., 2008, 340(2), 861–875. http://dx.doi.org/10.1016/j.jmaa.2007.09.021
  • [2] Chen, B.-Y., Classification of marginally trapped surfaces of constant curvature in Lorentzian complex plane, Hokkaido Math. J., 2009, 38(2), 361–408. http://dx.doi.org/10.14492/hokmj/1248190082
  • [3] Chen, B.-Y., Black holes, marginally trapped surfaces and quasi-minimal surfaces. Tamkang J. Math., 2009, 40(4), 313–341.
  • [4] Chen, B.-Y., Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. http://dx.doi.org/10.1142/8003
  • [5] Chen, B.-Y., Dillen, F., Classification of marginally trapped Lagrangian surfaces in Lorentzian complex space forms, J. Math. Phys., 2007, 48(1), 013509, 23 pp.; Erratum, J. Math. Phys., 2008, 49(5), 059901, 1p. http://dx.doi.org/10.1063/1.2424553
  • [6] Chen, B.-Y., Garay, O., Classification of quasi-minimal surfaces with parallel mean curvature vector in pseudo-Euclidean 4-space \(\mathbb{E}_2^4 \) , Result. Math., 2009, 55(1–2), 23–38. http://dx.doi.org/10.1007/s00025-009-0386-9
  • [7] Chen, B.-Y., Mihai, I., Classification of quasi-minimal slant surfaces in Lorentzian complex space forms, Acta Math. Hungar., 2009, 122(4), 307–328. http://dx.doi.org/10.1007/s10474-008-8033-6
  • [8] Chen, B.-Y., Van der Veken, J., Marginally trapped surfaces in Lorentzian space with positive relative nullity, Class. Quantum Grav., 2007, 24(3), 551–563. http://dx.doi.org/10.1088/0264-9381/24/3/003
  • [9] Chen, B.-Y., Van der Veken, J., Spatial and Lorentzian surfaces in Robertson-Walker space times, J. Math. Phys., 2007, 48(7), 073509, 12 pp. http://dx.doi.org/10.1063/1.2748616
  • [10] Chen, B.-Y., Van der Veken, J., Classification of marginally trapped surfaces with parallel mean curvature vector in Lorenzian space forms, Houston J. Math., 2010, 36(2), 421–449.
  • [11] Chen, B.-Y., Yang, D., Addendum to “Classification of marginally trapped Lorentzian flat surfaces in \(\mathbb{E}_2^4 \) and its application to biharmonic surfaces,” J. Math. Anal. Appl., 2010, 361(1), 280–282. http://dx.doi.org/10.1016/j.jmaa.2009.08.061
  • [12] Ganchev, G., Milousheva, V., Chen rotational surfaces of hyperbolic or elliptic type in the four-dimensional Minkowski space, C. R. Acad. Bulgare Sci., 2011, 64(5), 641–652.
  • [13] Ganchev, G., Milousheva, V., An invariant theory of marginally trapped surfaces in the four-dimensional Minkowski space, J. Math. Phys., 2012, 53(3), 033705, 15 pp. http://dx.doi.org/10.1063/1.3693976
  • [14] Haesen, S., Ortega, M., Boost invariant marginally trapped surfaces in Minkowski 4-space, Classical Quantum Gravity, 2007, 24(22), 5441–5452. http://dx.doi.org/10.1088/0264-9381/24/22/009
  • [15] Haesen, S., Ortega, M., Marginally trapped surfaces in Minkowski 4-space invariant under a rotational subgroup of the Lorentz group, Gen. Relativity Gravitation, 2009, 41(8), 1819–1834. http://dx.doi.org/10.1007/s10714-008-0754-x
  • [16] Haesen, S., Ortega, M., Screw invariant marginally trapped surfaces in Minkowski 4-space, J. Math. Anal. Appl., 2009, 355(2), 639–648. http://dx.doi.org/10.1016/j.jmaa.2009.02.019
  • [17] Liu H., Liu G., Hyperbolic rotation surfaces of constant mean curvature in 3-de Sitter space, Bull. Belg. Math. Soc. Simon Stevin, 2000, 7(3), 455–466.
  • [18] Liu H., Liu G., Weingarten rotation surfaces in 3-dimensional de Sitter space, J. Geom., 2004, 79(1–2), 156–168. http://dx.doi.org/10.1007/s00022-003-1567-4
  • [19] Penrose, R. Gravitational collapse and space-time singularities, Phys. Rev. Lett., 1965, 14, 57–59. http://dx.doi.org/10.1103/PhysRevLett.14.57
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0430-1
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