共查询到18条相似文献,搜索用时 93 毫秒
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本文中,我们研究了一类Schroedinger算子的第一特征值,给出了S^n 1中一类常平均曲率超曲面的特征,并得到了这种超曲面的谱几何,从而推广了第二作者的有关结果。 相似文献
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本文证明了如果S4中的具常平均曲率h的超曲面M与其具平均曲率h的等参超曲面M0(强)等谱,则M=M0. 相似文献
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TheIsometryofRiemannianManifoldtoaSphereZhaoPeibiao(赵培标)(Dept.ofMath.,AnhuiInstituteofFinance&Trade,233041)Abstract:Inthispap... 相似文献
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我们给出了欧氏椭球面$Q^{n+1}(c,d)$中平行超曲面的完全分类,并且证明了$Q^{n+1}(c,d)$中的超曲面是全脐的当且仅当它是平行的. 相似文献
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设M是单位球面S~(n 1)(1)中的n维(n■3)紧致连通定向超曲面,本文研究这种超曲面的曲率结构与拓扑性质,利用Lawson和Simons关于稳定k维流的不存在性与同调群消失定理,得到了曲率与拓扑的一个关系定理,从而对Cheng Q.M.所提出的一个分类问题从拓扑角度给出了一个肯定回答,并且部分肯定回答了Cheng的另一个问题. 相似文献
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ARemarkontheIntrinsicRigidityofCompactMinimalSubmanifoldsinASphere¥ShuShichang(舒世昌)(iaXingqin(贾兴琴)(XianyangTeachers'College,7... 相似文献
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Alain R. Veeravalli 《Geometriae Dedicata》1999,74(3):287-290
We focus our attention on compact hypersurfaces with Ricci curvature bounded from above and we give a sufficient condition for them to be spherical. This generalizes and completes previous results. 相似文献
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Quasi—Einstein Hypersurfaces in a Hyperbolic Space 总被引:1,自引:0,他引:1
§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.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1… 相似文献
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设M为Sn 1(1)中紧致极小超面Mn1,n2= Sn1nn1×Sn2nn2 Sn 1(1)为Sn 1(1)中的Clifford极小超曲面如果Specp( M) =specp( Mn1,n2) ,Specq( M) =specq( Mn1,n2) ,其中0≤p
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David Bleecker 《Geometriae Dedicata》1997,64(2):193-227
In 1955 N. Kuiper and J. Nash proved that given a C
embeddingF of a C
Riemannian n -manifold (M,g) in E
n+1 which is short in the sense that the metric induced by F is less thang, there is a C
1 isometric embedding which is arbitrarily C
0-close to F. We extend the Nash--Kuiper result for compact M to the case of deformations. In other words, we prove that given a continuous family of short C
embeddings
(
) of a compact Riemannian n-manifold M , there is an isometric deformation through C
1 embeddings which is C
0 -close to F. With more assumptions which are typically met in practice, this result is shown to hold in the more difficult case where F(s) is short for s>0 andF(0) is isometric. We use this to prove that if a C
convex hypersurface is sufficiently close to being planar in an average sense (e.g. an oblate spheroid in E
3 with axis ratio more than
, then it admits an isometric deformation which increases the enclosed volume. 相似文献