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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
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关于复射影空间的实极小超曲面 总被引:4,自引:1,他引:3
<正> 一、引言对于复射影空间的紧致实极小超曲面,Lawson H.B.和 Kon M.先后给出了第二基本形式长度平方(相当于超曲面的数量曲率)和截面曲率的 Pinching 定理.OkumuraM.又把[3]的结果推广到常平均曲率的实超曲面.本文的目的是进一步讨论这种量子化现象. 相似文献
4.
该文对 anti-de Sitter 空间H1n+1中的紧致类空超曲面建立了积分公式,并应用它们在常高阶平均曲率的条件下讨论了H1n+1中紧致类空超曲面的全脐问题. 相似文献
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本文证明了如果S4中的具常平均曲率h的超曲面M与其具平均曲率h的等参超曲面M0(强)等谱,则M=M0. 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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本文研究常曲率黎曼流形 S~(n+1)(c)中的共形平坦的极小超曲面 M~h,证明了下面结果.定理 设 M~h 是 n+1维常曲率黎曼流形 S~(n+1)(c)的共形平坦超曲面(n≥4),则 M~n是常数量曲率的极小超曲面的充要条件是:(1)M~n 的数量曲率 R=(n-1)c 时,M~n 是全测地超曲面,从而也有常曲率 c;(2)M~n 的数量曲率 R≠n(n-1)c 时,c>0和 M~n 局部可约为常曲率黎曼流形S~(n-1)(n/(n-1) c)与直线 R′的乘积.系,设 M~n 是具有非正常曲率 c 的黎曼流形 S~(n+1)(c)的共形平坦超曲面(n≥4),如果M~n 是常数量曲率的极小超曲面,则 M~n 是全测地超曲面。 相似文献
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Spacelike hypersurfaces with constant scalar curvature 总被引:1,自引:0,他引:1
In this paper, we shall give an integral equality by applying the operator □ introduced by S.Y. Cheng and S.T. Yau [7] to
compact spacelike hypersurfaces which are immersed in de Sitter space S
n
+1
1(c) and have constant scalar curvature. By making use of this integral equality, we show that such a hypersurface with constant
scalar curvature n(n-1)r is isometric to a sphere if r << c.
Received: 18 December 1996 / Revised version: 26 November 1997 相似文献
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In this paper, we shall give an integral equality by applying the operator □ introduced by S.Y. Cheng and S.T. Yau [7] to
compact spacelike hypersurfaces which are immersed in de Sitter spaceS
1
n+1
(c) and have constant scalar curvature. By making use of this integral equality, we show that such a hypersurface with constant
scalar curvaturen(n−1)r is isometric to a sphere ifr<c.
Research partially Supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and
Culture. 相似文献
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In this paper we characterize the spacelike hyperplanes in the Lorentz–Minkowski space L
n
+1 as the only complete spacelike hypersurfaces with constant mean curvature which are bounded between two parallel spacelike
hyperplanes. In the same way, we prove that the only complete spacelike hypersurfaces with constant mean curvature in L
n
+1 which are bounded between two concentric hyperbolic spaces are the hyperbolic spaces. Finally, we obtain some a priori estimates
for the higher order mean curvatures, the scalar curvature and the Ricci curvature of a complete spacelike hypersurface in
L
n
+1 which is bounded by a hyperbolic space. Our results will be an application of a maximum principle due to Omori and Yau, and
of a generalization of it.
Received: 5 July 1999 相似文献
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Jocelino Sato Vicente Francisco De Souza Neto 《Annals of Global Analysis and Geometry》2006,29(3):221-240
We classify the zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in the euclidean space ℝ
p+q+2, p,q > 1, analyzing whether they are embedded and stable. The Morse index of the complete hypersurfaces show the existence of embedded, complete and globally stable zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in ℝ
p+q+2, p+q≥ 7, which are not homeomorphic to ℝ
p+q+1. Such stable examples provide counter-examples to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature.
Mathematics Subject Classifications (2000): 53A10, 53C42,49005. 相似文献
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This paper gives a classification of complete hypersurfaces with nonzero constant mean curvature and constant quasi-Gauss-Kronecker curvature in the hyperbolic space H4(-1),whose scalar curvature is bounded from below. 相似文献
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We classify hypersurfaces of the hyperbolic space ?n+1(c) with constant scalar curvature and with two distinct principal curvatures. Moreover, we prove that if Mn is a complete hypersurfaces with constant scalar curvature n(n ? 1) R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n? 1, then R ≥ c. Additionally, we prove two rigidity theorems for such hypersurfaces. 相似文献
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Non-spherical hypersurfaces inE
4 with non-zero constant mean curvature and constant scalar curvature are the only hypersurfaces possessing the following property: Its position vector can be written as a sum of two non-constant maps, which are eigenmaps of the Laplacian operator with corresponding eigenvalues the zero and a non-zero constant. 相似文献
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In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form M n+1(c). We obtain some rigidity results of nonnegative sectional curvature hypersurfaces M n+1(c) with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product S k (a) × S n-k (√1 ? a 2), 1 ≤ k ≤ n ? 1, in S n+1(1) and the Riemannian product H k (tanh2 r ? 1) × S n-k (coth2 r ? 1), 1 ≤ k ≤ n ? 1, in H n+1(?1). 相似文献
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Krzysztof Andrzejewski Pawe? G. Walczak 《Differential Geometry and its Applications》2011,29(6):723-729
In this paper, we study hypersurfaces with constant rth mean curvature Sr. We investigate the stability of such hypersurfaces in the case when they are leaves of a codimension one foliation. We also generalize recent results by Barros and Sousa, concerning conformal fields, to an arbitrary manifold. Using this we show that normal component of a Killing field is an rth Jacobi field of a hypersurface with Sr+1 constant. Finally, we study relations between rth Jacobi fields and vector fields preserving a foliation. 相似文献
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Qing-Ming Cheng 《manuscripta mathematica》1994,82(1):149-160
In this paper, we prove that the hyperbolic cylinderH
1(c
1)×H
2(c
2) is the only complete maximal spacelike hypersurfaces inH
1
4
(c) with nonzero constant Gauss-Kronecker curvature and give a characterization of complete maximal spacelike hypersurfaces
ofH
1
4
(c) with constant scalar curvature.
The project Supported by NNSFC, FECC and CPF 相似文献