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61.
A characterization of the Clifford torus 总被引:7,自引:0,他引:7
Qing-Ming Cheng Susumu Ishikawa 《Proceedings of the American Mathematical Society》1999,127(3):819-828
In this paper, we prove that an -dimensional closed minimal hypersurface with Ricci curvature of a unit sphere is isometric to a Clifford torus if , where is the squared norm of the second fundamental form of .
62.
Gabjin Yun 《Geometriae Dedicata》2002,89(1):133-139
Let M
n
, n 3, be a complete oriented immersed minimal hypersurface in Euclidean space R
n+1. We show that if the total scalar curvature on M is less than the n/2 power of 1/C
s
, where C
s
is the Sobolev constant for M, then there are no L
2 harmonic 1-forms on M. As corollaries, such a minimal hypersurface contains no nontrivial harmonic functions with finite Dirichlet integral and so it has only one end. This implies finally that M is a hyperplane. 相似文献
63.
A. V. Loboda 《Mathematical Notes》1998,64(6):761-766
The coincidence of two definitions of local homogeneity for real-analytic hypersurfaces in two-dimensional complex spaces is proved. It is shown that if any two germs of a Levi nondegenerate nonspherical surfaceM are equivalent, then this surface has a local Lie group structure:M then acts transitively on itself by left shifts, and each such shift is a local holomorphic transformation of 2.Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 881–887, December, 1998.This paper was conceived and largely written during author's visits to the Universities of West Ontario and Regina (Canada) under the kind invitation of Professors B. Gilligan and A. Bowen. The author wishes to express his great indebtedness to them for providing excellent conditions for work and gratitude for useful discussions. 相似文献
64.
研究(5维洛伦兹球面)中的Ⅲ型洛伦兹等参超曲面。证明了最小多项式为(λ-1)3(λ+1)洛伦兹等参超曲面~M局地被五个一元函数C1(u),C2(u),C3(u),C4(u),C5(u)所唯一确定。并给出了M~的解析表达式。还说明了S51中的任何Ⅲ型洛伦兹等参超曲面M局部地与最小多项式为(λ-1)3(λ+1)的某 相似文献
65.
Alan D. Rendall 《Mathematische Nachrichten》1998,193(1):111-118
Restrictions are obtained on the topology of a compact divergence - free null hypersurface in a four-dimensional Lorentzian manifold whose Ricci tensor is zero or satisfies some weaker conditions. This is done by showing that each null hypersurface of this type can be used to construct a family of three - dimensional Riemannian metrics which collapses with bounded curvature and applying known results on the topology of manifolds which collapse. The result is then applied to general relativity, where it implies a restriction on the topology of smooth compact Cauchy horizons in spacetimes with various types of reasonable matter content. 相似文献
66.
In this paper, we make estimates for the radius of balls contained in some component of the complementary of a complete hypersurface
into a space form, generalizing and improving analogous radius estimates for embedded compact hypersurfaces obtained by Blaschke,
Koutroufiotis and the authors. The results are obtained using an algebraic lemma and a tangency principle related with the
length of the second fundamental form. The algebraic lemma also is used to improve a result for graphs due to Hasanis–Vlachos.
The first author dedicates this work to his parents José (in memoriam) and Herondina 相似文献
67.
I. A. Chel’tsov 《Mathematical Notes》2000,68(1):113-119
The objective of this paper is to study the birational structure of smooth hypersurfaces of degreeN in
by examining properties of moving log pairs on them.
Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp 131–138, July, 2000. 相似文献
68.
Oliver C. Schnurer 《Transactions of the American Mathematical Society》2003,355(2):655-663
We prove the existence of hypersurfaces with prescribed boundary whose Weingarten curvature equals a given function that depends on the normal of the hypersurface.
69.
J. Kenedy Martins 《Bulletin of the Brazilian Mathematical Society》2001,32(1):83-105
The invariants needed to decide when a pair of hypersurfaces ofS
6 orCP
n
are respectivelyG
2-congruent or holomorpic congruent are determined and this result is used to characterize the hypersurfaces of these spaces whose Hopf vector fields are also Killing fields. 相似文献
70.
FANG Fuquan 《数学年刊B辑(英文版)》2000,21(4):473-478
This note investigates the multiplicity problem of principal curvatures of equifocal hypersurfaces in simply connected rank
1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces
in the symmetric spaces.
Project supported by the National Natural Science Foundation of China (No. 19925104), RFDP and the Qiu-Shi Science and Technology
Foundation. 相似文献