| Quasi—Einstein Hypersurfaces in a Hyperbolic Space |
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| 引用本文： | 赵培标,宋鸿藻.Quasi—Einstein Hypersurfaces in a Hyperbolic Space[J].数学季刊,1998,13(2):49-52. |
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| 作者姓名： | 赵培标 宋鸿藻 |
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| 摘 要： | §1. IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj, (i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom1]and2]:Rij=R-Tn-1…
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| 关 键 词： | 双曲空间 拟爱因斯坦超曲面 黎曼流形 |
Quasi Einstein Hypersurfaces in a Hyperbolic Space |
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| Zhao PeibiaoSong Hongzao.Quasi Einstein Hypersurfaces in a Hyperbolic Space[J].Chinese Quarterly Journal of Mathematics,1998,13(2):49-52. |
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| Authors: | Zhao PeibiaoSong Hongzao |
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| Institution: | [1]Auhui [2]Institute |
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| Abstract: | In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough. |
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| Keywords: | quasi Einstein hypersurface hyperbolic space totally umbilic hypersurface |
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