共查询到19条相似文献,搜索用时 15 毫秒
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本文研究了复空间形式中具有常数量曲率的全实子流形.利用一种自伴算子,得到了这类子流形关于第二基本形式模长平方的积分不等式. 相似文献
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本文研究了复射影空间中具有常数量曲率的完备全实子流形的问题.利用丘成桐的广义极大值原理和自伴随算子,获得了这类子流形的某些内蕴刚性定理. 相似文献
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Let f : M^n→S^n 1真包含于R^n 2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n 1)-dimensional unit sphere S^n 1. Denote by S^n 1 the upper closed hemisphere. If f(M^n)包含于S ^n 1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. 相似文献
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1IntroductionItiswell-knownthattheclassicalWeierstrass-EnneperrepresentationformuladescribeschinalsurfacesinEuclidean3-spaceR3intermsoftheirGaussmapsandauxiliaryholomorphicfunctions[1].Moregenerally,aremarkablerepresentationforlllulahasbeendiscoveredbyKenmotsu[2]forarbitrarysurfaCesinR3withnonvallishingmeancurvature,whichdescribesthesesurfacesintermsoftheirGaussmapsandmeancurvaturefunctions.Recently,Konopelchenko[31rediscoveredthisrepresentationformulaindifferentbutequivalentformillconnect… 相似文献
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以把调和态射看作等距浸入的单位法投影的问题为背景,研究了具有共形第二基本形式的子流形,论证了具有共形第二基本形式的高维子流形,一般不是由极小点和全脐点构成,这和曲面的情形形成了鲜明的对照。也给出了常曲率空间中具有平行中曲率的奇数维子流形的一个完全分类。 相似文献
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COMPLETE HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A SPECIAL KIND OF LOCALLY SYMMETRIC MANIFOLD
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Yingbo Han & Shuxiang Feng 《分析论及其应用》2012,28(2):189-200
In this paper, we investigate n-dimensional complete and orientable hypersufaces M n (n ≥ 3) with constant normalized scalar curvature in a locally symmetric manifold. Two rigidity theorems are obtained for these hypersurfaces. 相似文献
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Xu Hongwei Zhang Wei 《高校应用数学学报(英文版)》2007,22(3):371-377
The geometric properties for Gaussian image of submanifolds in a sphere are investigated.The computation formula,geometric equalities and inequalities for the volume of Gaussian image of certain submanifolds in a sphere are obtained. 相似文献
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ZUO DAFENG CHEN QING CHENG YI Department of Mathematics University of Science Technology of China Hefei China Department of Mathematical Sciences Tsinghua University Beijing China. Department of Mathematics University of Science Technology of China Hefei China. Department of Mathematics University of Science Technology of China Hefei China. 《数学年刊B辑(英文版)》2005,26(3)
By using dressing actions of the G(n1,n-1)1,1-system, the authors study geometric transformations for flat time-like n-submanifolds with flat, non-degenerate normal bundle in anti-de Sitter space H1(2n-1)(-1), where G(n-1,n-1)1,1 = O(2n - 2, 2)/O(n - 1,1)×O(n-1, 1). 相似文献
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In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed. 相似文献
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<正> 在歐氏空間E_(m+1)中的安裝及變形問題在近一世紀的幾何學者的工作中得到了解决,而所確定的V_m E_(m+1)一般是不能變形的。就是說,能够變形的只是狹窄的一類超曲面.運用了外微分形式的方法,很詳細地綜合了這些工作,並且完全地給出 相似文献
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In this article, it is proved that there doesn’t exist any nonsingular holomorphic sphere in complex Grassmann manifold G(2, 5) with constant curvature k = 4/7, 1/2, 4/9. Thus, from [7] it follows that if φ : S2 → G(2, 5) is a nonsingular holomorphic curve with constant curvature K, then, K = 4, 2, 4/3, 1 or 4/5. 相似文献
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黄宣国 《数学年刊A辑(中文版)》2002,(2)
M是Sn+1(1)内紧致嵌入凸超曲面.M分Sn+1(1)为两个连通区域Ω1和Ω2.Ω1=M和Ω1是凸的.本文估计了Ω1的Laplace算子的第一特征值的下界. 相似文献
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利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理. 相似文献