共查询到20条相似文献,搜索用时 109 毫秒
1.
主要研究了拟常曲率空间中具有常平均曲率的完备超曲面,得到了这类超曲面全脐的一个结果.即若Nn+1的生成元η∈TM,且a-2|b|=c(常数)>0,则当S<2 n-1~(1/2)(a-2|b|)时,M为全脐超曲面. 相似文献
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本文的目的在于给出一种方法,它可以看作通常的 Bochner 技巧的改进,据此我们证明了 CP~n 的完备全实具有平行中曲率向量和强正截曲率的 n 维子流形是全测地的. 相似文献
3.
本文的目的在于给出一种方法,它可以看作通常的 Bochner 技巧的改进,据此我们证明了 CP~n 的完备全实具有平行中曲率向量和强正截曲率的 n 维子流形是全测地的. 相似文献
4.
复空间形式中常数量曲率的完备全实伪脐子流形 总被引:1,自引:0,他引:1
设CNnc是具有常全纯截面曲率c(≤O)的复n维的复空间形式,Mn是CNnc中常数量曲率的完备全实伪脐子流形,R,‖h‖2分别表示Mn的标准数量曲率和第二基本形式模长的平方.假设R≥c/4.利用丘成桐的广义极大值原理和自伴随算子研究了关于‖h‖2的pinching问题,得到了两个Mn成为全测地或全脐的刚性定理. 相似文献
5.
本文研究了具有非负Ricci曲率和次大体积增长的完备黎曼流形的拓扑结构问题.利用Toponogov型比较定理及临界点理论,获得了流形具有有限拓扑型的结果,推广了H.Zhan和Z.Shen的定理,并且还证明了该流形的基本群是有限生成的. 相似文献
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本文对Reinhardt域D(k)在不变Kahler度量下的全纯截曲率的具体表达式给出详细证明.并构造了一个不变的完备的不小于Bergman 度量的D(k)的Kahler度量,使得其全纯截曲率的上界是一个负常数,从而得到域D(k)的关于Bergman 度量和 Kobayashi度量的比较定理. 相似文献
9.
张宗劳 《数学年刊A辑(中文版)》1989,(1)
本文借助于J.Cheeger和D.Gromoll对非负曲率完备流形建立的紧全凸集族结构,研究了这种流形上射线之间的相互关系。另外,还得到了涉及Soul的一个结果。 相似文献
10.
<正> 在前一文[1]中,作者曾用折线逼近曲线,以研究曲綫的全曲率.本文目的,是要証明一个关于用光滑曲綫逼近具有有限个角点的曲线的定理.藉此定理之助,关于光滑曲綫全曲率的許多已知的定理,如Fenchel定理等,都可以推广到具有有限个角点的曲綫去. 本文的方法和結果都可以毫无困难地推广到高維欧几里得空間中去,但为簡单起見,我們只就3維欧几里得空間的情况来討論.文中所述及的曲綫是分段光滑的,且除有限 相似文献
11.
We give a complete classification of complete noncompact oriented surfaces with nonnegative Gaussian curvature and finite total mean curvature in R3. 相似文献
12.
Xuan Hien Nguyen 《Journal of Geometric Analysis》2013,23(3):1379-1426
We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position. 相似文献
13.
Takumi Yokota 《Geometriae Dedicata》2008,133(1):169-179
In this paper, we consider the behavior of the total absolute and the total curvature under the Ricci flow on complete surfaces
with bounded curvature. It is shown that they are monotone non-increasing and constant in time, respectively, if they exist
and are finite at the initial time. As a related result, we prove that the asymptotic volume ratio is constant under the Ricci
flow with non-negative Ricci curvature, at the end of the paper.
相似文献
14.
The main result of this paper states that the traceless second fundamental tensor A0 of an n-dimensional complete hypersurface M, with constant mean curvature H and finite total curvature, M |A0|n dvM < , in a simply-connected space form
(c), with non-positive curvature c, goes to zero uniformly at infinity. Several corollaries of this result are considered: any such hypersurface has finite index and, in dimension 2, if H
2 + c > 0, any such surface must be compact. 相似文献
15.
常曲率空间中具平行平均曲率向量的子流形 总被引:6,自引:0,他引:6
本文利用第二基本形式的长度平方和平均曲率的关系研究常曲率空间中具平行平均曲率向量的子流形为全脐的pinching问题,获得了一定条件下的最佳pinching区间,并确定了phincning区间端点处对应非全脐子流形的分类. 相似文献
16.
Yi Bing SHEN Xiao Hua ZHU 《数学学报(英文版)》2005,21(3):631-642
By using curvature estimates, we prove that a complete non-compact hypersurface M with constant mean curvature and finite L^n-norm curvature in R^1+1 must be minimal, so that M is a hyperplane if it is strongly stable. This is a generalization of the result on stable complete minimal hypersurfaces of R^n+1. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite L^1-norm curvature in R^1+1 are considered. 相似文献
17.
Philippe Castillon 《Annals of Global Analysis and Geometry》1999,17(6):563-579
In this work we determine the essential spectrum of the stability operator of a submanifold of the hyperbolic space with constant mean curvature h < 1 and finite total curvature. In some particular cases, we also give a bound on the number of eigenvalues which are below the essential spectrum. 相似文献
18.
The purpose of this paper is to prove that alocally strongly convex, Euclidean complete surface with constantaffine mean curvature is also affine complete. Consequently weobtain a classification of locally strongly convex, Euclideancomplete surfaces with constant affine mean curvature. 相似文献
19.
Yuanlong XIN 《数学年刊B辑(英文版)》2008,29(2):121-134
In this paper,the mean curvature flow of complete submanifolds in Euclidean space with convex Gauss image and bounded curvature is studied.The confinable property of the Gauss image under the mean curvature flow is proved,which in turn helps one to obtain the curvature estimates.Then the author proves a long time existence result.The asymptotic behavior of these solutions when t→∞is also studied. 相似文献
20.
Let(M~n, g)(n ≥ 3) be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R?m the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R?m goes to zero uniformly at infinity if for p ≥ n, the L~p-norm of R?m is finite.As applications, we prove that(M~n, g) is compact if the L~p-norm of R?m is finite and R is positive, and(M~n, g) is scalar flat if(M~n, g) is a complete noncompact manifold with nonnegative scalar curvature and finite L~p-norm of R?m. We prove that(M~n, g) is isometric to a spherical space form if for p ≥n/2, the L~p-norm of R?m is sufficiently small and R is positive.In particular, we prove that(M~n, g) is isometric to a spherical space form if for p ≥ n, R is positive and the L~p-norm of R?m is pinched in [0, C), where C is an explicit positive constant depending only on n, p, R and the Yamabe constant. 相似文献