共查询到19条相似文献,搜索用时 62 毫秒
1.
Hypersurfaces with Constant Mean Curvature in Space FormsHypersurfaceswithConstantMeanCurvatureinSpaceForms¥SongHongzao;HuZej... 相似文献
2.
3.
Rafael López 《Geometriae Dedicata》1999,76(1):81-95
We prove that a spacelike surface in L3 with nonzero constant mean curvature and foliated by pieces of circles in spacelike planes is a surface of revolution. When the planes containing the circles are timelike or null, examples of nonrotational constant mean curvature surfaces constructed by circles are presented. Finally, we prove that a nonzero constant mean curvature spacelike surface foliated by pieces of circles in parallel planes is a surface of revolution. 相似文献
4.
1.IntroductionTheproblemsofinfinitesimalrigidityandisometricdeformationhavebeenextensivelyin-vestigatedforsurfacesinthreedimensionalEuclideanspaceE'.See,forexample,A.SvecL1]'E.Kann[2j,ZhouJiazu[3Jandthepapers[4j,[5J,[6JbyYangWenmao3also,KobayashiandNomizu[7].ThefirstauthorandZhangGaoyonggeneralizedthetheoryofinfinitesimali-sometriesofsurfacesinE3tothehypersurfacesimmersedinaspaceofconstantcurvature[8j.K.Tenenblat[9]andR.A.GoldsteinandP.J.Ryan[1o]studiedtheinfinitesimalI-isometryfors… 相似文献
5.
Let M be an n(≥3)-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1 (n+1) (1) with constant mean curvature and non negative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥1. When 2(n-1)~(1.2)/n < H < 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder. 相似文献
6.
An overview of the various transformations of isothermic surfaces and their interrelations is given using aquaternionic formalism. Applications to the theory of cmc-1 surfaces inhyperbolic space are given and relations between the two theories are discussed. Within this context, we give Möbius geometric characterizations for cmc-1 surfaces in hyperbolic space and theirminimal cousins. 相似文献
7.
In [1], S. T. Yau proved the following theorems: (1) If M is compact hyper-surface with constant mean curvature and non-negative Ricci curvature in the Eucli-dean space, then M is umbilical. (2) If M is compact hypersurface with constantscalar curvature in hyperbolic space form and M has positive sectional curvature, thenM is totally umbilical. In this paper, we shall generalize the theorems as follows 相似文献
8.
Makoto Sakaki 《Results in Mathematics》2014,66(3-4):343-362
Deforming rotation surfaces with constant mean curvature in S 3 and H 3 to S 3 × R and H 3 × R respectvely, we give four classes of surfaces with mean curvature vector of constant length in S 3 × R and H 3 × R. We have complete minimal surfaces in S 3 × R and H 3 × R. Also we obtain minimal 2-tori in S 3 × S 1, some of which are embedded. 相似文献
9.
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
10.
§1. T. Otsuki [1] studied the minimal hypersurface V~n of a Riemannian manifold S~(n 1) of constant curvature if the number of the distinct principal normal curvatures is two and the multiplicities of them are at least two. He proved that V~n is locally the Riemannian prodruct S~(?)×S~(?) of two Riemannian manifolds S~(?) and S~(?) of constant curvature, where ι_1 and ι_2 are these multiplicities, respectively. In the present paper S~m denotes an m-dimensional Riemannian manifold of 相似文献
11.
本文利用共形度量高斯曲率的估计研究了三维空间形式N^3(C)中具常平均曲率曲面的区域稳定性。 相似文献
12.
Ronaldo F. de Lima 《Annals of Global Analysis and Geometry》2001,20(4):325-343
Maximum principles at infinity generalize Hopf's maximum principle for hypersurfaces with constant mean curvature in R
n
. We establish such a maximum principle for parabolic surfaces in R3 with nonzero constant mean curvature and bounded Gaussian curvature. 相似文献
13.
Rafael Lopez 《Geometriae Dedicata》1997,66(3):255-263
This paper proves that an embedded compact surface in the Euclidean space with constant mean curvature H bounded by a circle of radius 1 and included in a slab of width
is a spherical cap. Also, we give partial answers to the problem when a surface with constant mean curvature and planar boundary lies in one of the halfspaces determined by the plane containing the boundary, exactly, when the surface is included in a slab. 相似文献
14.
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
15.
Jorge Herbert S. De Lira 《Geometriae Dedicata》2002,93(1):11-23
The existence is proved of radial graphs with constant mean curvature in the hyperbolic space H
n+1 defined over domains in geodesic spheres of H
n+1 whose boundary has positive mean curvature with respect to the inward orientation. 相似文献
16.
17.
本文估计了空间形式Nn+1(c)中常平均曲率超曲面上共形度量的曲率上界,并用其研究了Nn+1(c)中常平均曲率超曲面的强稳定性. 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.
Baris Coskunuzer 《Geometriae Dedicata》2006,118(1):157-171
We study the constant mean curvature (CMC) hypersurfaces in
whose asymptotic boundaries are closed codimension-1 submanifolds in
. We consider CMC hypersurfaces as generalizations of minimal hypersurfaces. We naturally generalize some notions of minimal hypersurfaces like being area-minimizing, convex hull property, exchange roundoff trick to CMC hypersurface context. We also give a generic uniqueness result for CMC hypersurfaces in hyperbolic space. 相似文献