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Anti-de Sitter空间中紧致类空超曲面的积分公式 被引量:1

Integral Formula for Compact Space-like Hypersurfaces in Anti-de Sitter Space
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摘要 讨论了anti-de Sitter空间中紧致类空超曲面的积分公式,得到该类空超曲面是全脐的充要条件. The integral formula for compact space-like hypersurfaces in anti-de Sitter space is discussed and a necessary and sufficient condition is obtained which guarantees this space-like hypersurface is totally umbilical.
作者 高耀文
出处 《甘肃科学学报》 2009年第3期1-4,共4页 Journal of Gansu Sciences
关键词 积分公式 紧致类空超曲面 anti—de SITTER空间 integral formula compact space-like hypersurface anti-de Sitter space
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参考文献8

  • 1Goddard A J. Some Remarks on the Existence of Space-like Hypersurfaces of Constant Mean Curvature[J]. Math Proc Cambridge Phi Soc, 1977,82:489-495.
  • 2Cheng Q M, Ishikawa S. Space-like Hypersurfaces with Constant Scalar Curvature[J]. Manuscripta Math, 1998,99 : 499-505.
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  • 5李海中,陈维桓.De Sitter空间中紧致类空超曲面的积分公式及其Goddard猜想的应用[J].数学学报(中文版),1998,41(4):807-810. 被引量:9
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二级参考文献7

  • 1Goddard A J.Some remarks on the existence of space-like hypersurfaces of constant mean curvature.Math Proc Cambrige Phil Soc,1977,82:489-495
  • 2Montiel S.An integral inequality for compact space-like hypersurfaces in de Sitter space and applications to the case of constant mean curvature.Indiana Vniv Math J,1988,37:909-917
  • 3Aledo J A,Alías L J,Romero A.Integral formulas for compact space-like hypersurfaces in de Sitter space:Applications to the case of constant higher order mean curvature.Geom Phy,1999,31:195-208
  • 4Aledo J A,Alías L J.Curvature properties of compact spacelike hypersurfaces in de Sitter space.Differential Geom Appl,2001,14:137-149
  • 5Ulo Lumiste.Semi-parallel time-like surfaces in Lorentzian spacetime forms.Differential Geom Appl,1997,7:59-74
  • 6Hardy G,Littlewood J E,Poyla G.Inequalities.Cambridge:Cambridge University Press,1952
  • 7李海中,陈维桓.De Sitter空间中紧致类空超曲面的积分公式及其Goddard猜想的应用[J].数学学报(中文版),1998,41(4):807-810. 被引量:9

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