共查询到19条相似文献,搜索用时 62 毫秒
1.
关于局部对称空间中的伪脐子流形 总被引:8,自引:0,他引:8
本文讨论了局部对称完备黎曼流形中的紧致伪脐子流形,且具有平行平均山率向量场。得到了这类子流形成为全脐子流形及其余维数减小的几个拼挤定理。 相似文献
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研究近拟常曲率黎曼流形中的紧致伪脐子流形,利用活动标架法,得到了这类子流形的Simons型积分不等式及其刚性定理. 相似文献
3.
聂昌雄 《数学年刊A辑(中文版)》2015,36(1):59-68
[Nie C X,Wu C X,Regular submanifolds in the conformal space Q_p~n,ChinAnn Math,2012,33B(5):695-714]中研究了共形空间Q_s~n中的正则子流形,并引入了共形空间Q_s~n中的子流形理论.本文作者将分类共形空间Q_s~n中的Blaschke拟全脐子流形,证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;反之,共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.这一结论可看作是共形空间Q_s~n中共形迷向子流形分类定理的推广. 相似文献
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全脐子流形的一个特征 总被引:7,自引:0,他引:7
吴炳烨 《数学年刊A辑(中文版)》1994,(3)
1974年M.Okumura证明[1]:设Mn(n≥3)为n+1维单位球面Sn+1的紧致常平均曲率超曲面,若其第二基本形式的模长平方则Mn为全脐超曲面,其中H为平均曲率.本文目的是把限制常数改为,而且对于余维数大于1的情况也有类似的结果. 相似文献
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本文讨论了Sasakian空间型的C-全实伪脐子流形,给出关于第二基本形式长度的一个Pinching定理。 相似文献
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本文讨论C循环空间中的全脐子流形,证明了该子流形成为射影平坦或共圆平坦的充分必要条件是它又是爱因斯坦空间,这一结果推广了[1,2]中的相应结论。 相似文献
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The main result obtaind in this paper is that :Let M be a totally umbilical submanifolds in Riemannian manifold N. If the Weyl conformal curvature tensor for N satisfies the following condition: ▽xC=ω(X)C, for some 1-form ω and any vector field X in M, then M is con-formally flat or it is totally geodesic . 相似文献
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设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画;
然后
分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的
微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为
$A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件. 相似文献
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In this paper, an estimate of the constant scalar curvature of a compact non- minimal pseudo-umbilical Lagrangian submanifold in CP3 is obtained. As its application, we prove that compact Einstein pseudo-umbilical Lagrangian submanifolds in CP3 must be minimal. 相似文献
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Henri Anciaux 《Geometriae Dedicata》2006,120(1):37-48
We give new examples of self-shrinking and self-expanding Lagrangian solutions to the Mean Curvature Flow (MCF). These are Lagrangian submanifolds in
, which are foliated by (n − 1)-spheres (or more generally by minimal (n − 1)-Legendrian submanifolds of
), and for which the study of the self-similar equation reduces to solving a non-linear Ordinary Differential Equation (ODE). In the self-shrinking case, we get a family of submanifolds generalising in some sense the self-shrinking curves found by Abresch and Langer. 相似文献
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We obtain some equations for Hamiltonian-minimal Lagrangian surfaces in CP
2 and give their particular solutions in the case of tori. 相似文献
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关于复射影空间中的全实伪脐子流形 总被引:2,自引:1,他引:1
设$M^n$是复射影空间${\bf C}P^{n+p}$中的全实子流形. 本文研究$M^n$的平行脐性法向量场在法丛中的位置. 在$p>0$的情形通过选取合适的标架场, 得到具有平行平均曲率向量的全实伪脐子流形关于第二基本形式模长平方的一个Pinching定理. 相似文献
15.
Robert L. BRYANT 《数学年刊B辑(英文版)》2006,27(1):95-112
Abstract Let SO(n) act in the standard way on ℂn and extend this action in the usual way to ℂn+1 = ℂ ⊕ ℂn.
It is shown that a nonsingular special Lagrangian submanifold L ⊂ ℂn+1 that is invariant under this SO(n)-action intersects the fixed ℂ ⊂ ℂn+1 in a nonsingular real-analytic arc A (which may be empty). If n > 2, then A has no compact component.
Conversely, an embedded, noncompact nonsingular real-analytic arc A ⊂ ℂ lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A.
The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gérard and Tahara to prove the existence of the extension.
* Project supported by Duke University via a research grant, the NSF via DMS-0103884, the Mathematical Sciences Research Institute,
and Columbia University.
(Dedicated to the memory of Shiing-Shen Chern, whose beautiful works and gentle encouragement have had the most profound influence
on my own research) 相似文献
16.
本文对于局部对称黎曼流形中的伪脐点子流形给出了一个积分不等式,推广了Chen,B.Y.的一个相应的结果. 相似文献
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In this paper we show how to embed a time slice of the Schwarzchild spacetime that models the outer space around a massive star, as a Lagrangian submanifold invariant under the standard action of the special orthogonal group on complex Euclidean space. This result is generalized for rotationally invariant metrics that can be considered as higher-dimensional versions of Schwarzchild's and these submanifolds are locally characterized as the only ones with zero scalar curvature inside the above family. 相似文献
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复射影空间中的完备全实伪脐子流形 总被引:2,自引:0,他引:2
Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn+p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results. 相似文献