共查询到19条相似文献,搜索用时 78 毫秒
1.
设M^n是De Sitter空间S1^n+1中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面,若S≤2(n-1)^1/2,则M^n是等参超曲面。 相似文献
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本文把[1]的结论推广到超曲面是完备的情形,即我们证明了:设M3是单位球面S4(1)中常平均曲率及常数量曲率的完备超曲面。若S≤H2+6,则S只能等于1/3H2,3/4H2—1/4(H4+8H2)1/2+3,(3/4)H2+1/4(H4+8H2)1/2相似文献
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本文讨论复射影空间中曲率齐性实超曲面,在适当条件下证明了它与复射影空间中等参超曲面等价,因此得到它的局部结构。 相似文献
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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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若超曲面的Laguerre形式为零且Laguerre第二基本形式的特征值(称为Laguerre主曲率)为常数,则称超曲面为Laguerre等参超曲面.对R~6中的Laguerre等参超曲面进行了研究,得到了分类定理. 相似文献
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傅吉祥 《数学年刊A辑(中文版)》2000,(1)
本文研究了CPn中的弱等焦Hopf超曲面的分类,弱等焦超曲面首先是由滕楚莲与Thorbergsson在[13]中引入的,设 M是 CPn中的弱等焦 Hopf超曲面,则 M的不同焦半径的个数是 2,4或6;并且当 g= 2或 4时, M在 CPn中是等参的;当 g= 6时,n= 3,M=π-1(M)与 S7中的等参超曲面不Lie等价,此处π:S7→CP3是Hopf纤维化. 相似文献
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本文研究了 CPn中的弱等焦Hopf超曲面的分类,弱等焦超曲面首先是由滕楚莲与Thorbergsson在[13]中引入的.设M是CPn中的弱等焦Hopf超曲面,则M的不同焦半径的个数是2,4或6;并且当g=2或4时,M在CPn中是等参的;当g=6时,n=8,(M-)=π-1(M)与S7中的等参超曲面不Lie等价,此处π:S7→CP3是Hopf纤维化. 相似文献
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本文给出了近K?hler球面S6中具有常数K?hler角和常数曲率的极小曲面的例子,同时证明了两个唯一性定理. 相似文献
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The purpose of this paper is to make clear the so-called Nomizu problem, whether it is possible to find examples of space-like
isoparametric hypersurfaces in H
1
n+1 with more than two distinct principal curvatures. It is proved that a space-like isoparametric hypersurface in H
1
n+1 or S
1
n+1 can have at most two distinct principal curvatures. The authors present the classification and explicit analytic expressions
of such type of isoparametric hypersurfaces.
This paper was translated from J. Nanchang Univ. Nat. Sci. Ed., 2004, 28(2): 113–117 相似文献
12.
Linus Kramer 《Geometriae Dedicata》2000,79(3):321-339
In this third part, we consider those compact quadrangles which arise from isoparametric hypersurfaces of Clifford type and their focal manifolds. Sections 9–11 give a comprehensive introduction to these quadrangles from the incidence-geometric point of view. Section 10 contains also a new (algebraic) proof that these geometries are quadrangles.We determine which of these quadrangles have ovoids or spreads and also whether the normal sphere bundles of the focal manifolds admit sections, or whether they are topologically trivial. We give explicit geometric constructions for spreads, ovoids, and sections. 相似文献
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金天寿 《数学的实践与认识》2012,42(11):227-229
球面中等参超曲面理论近期获得蓬勃发展,它们在等距意义下的分类至今未完全解决,将证明球面中等参超曲面及其焦流形的微分同胚型有限. 相似文献
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Yu Ping SONG 《数学学报(英文版)》2014,(1)
An umbilical free oriented hypersurfacex:M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1(Ei(logρ)(r ri)Ei(r))ωi vanishes and Laguerre shape operator S=ρ1(S 1 rid)has constant eigenvalues.Hereρ=i(r ri)2,r=r1+r2+···+rn 1n 1is the mean curvature radius andSis the shape operator ofx.{Ei}is a local basis for Laguerre metric g=ρ2III with dual basis{ωi}and III is the third fundamental form ofx.In this paper,we classify all Laguerre isoparametric hypersurfaces in Rn(n3)with two distinct non-zero principal curvatures up to Laguerre transformations. 相似文献
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Let M4 be a closed minimal hypersurface in \(\mathbb{S}^5\) with constant nonnegative scalar curvature. Denote by f3 the sum of the cubes of all principal curvatures, by g the number of distinct principal curvatures. It is proved that if both f3 and g are constant, then M4 is isoparametric. Moreover, the authors give all possible values for squared length of the second fundamental form of M4. This result provides another piece of supporting evidence to the Chern conjecture. 相似文献
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给出了拟Gauss-Kronecker曲率的定义,并研究了S~4(1)中具有常拟Gauss-Kro-necker曲率的超曲面的特性。 相似文献