共查询到20条相似文献,搜索用时 62 毫秒
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张维Hao 《数学物理学报(A辑)》1992,12(2):136-139
设Ω是R~n(n≥2)中的单连通有界开集,其边界骪Ω是无限可微的封闭超曲面。设H(S)是Ω的平均曲率(n=2,H(s)是曲率)。假定s∈Ω,H(s)>0。记 则我们证明 ii)H_0/H_1≤(1-1/n)~2|Ω|/|Ω|~2 integral from n=Ω to (ds)/(H(s))~2, iii)|Ω|≤(1-1/n)integral from n=Ω to (ds)/H(s), 我们有如下未解决问题:是否成立不等式 相似文献
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本文证明了2型球面紧致超曲面是1型的,因而是质量对称的.换言之,不存在2型球面紧致超曲面,推广了文[2,3,4,5」中的结论. 相似文献
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张德燕 《高校应用数学学报(A辑)》2011,26(3):329-334
设Mn是de Sitter空间S1n+1+1(c)中具有第二基本形式模长平方‖h‖2是常数的类空超曲面,利用极大值原理得到了Mn是全脐超曲面的三个充分条件. 相似文献
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M是Sn+1(1)内紧致嵌入凸超曲面.M分Sn+1(1)为两个连通区域Ω1和Ω2. Ω1=M和Ω1是凸的.本文估计了Ω1的Laplace算子的第一特征值的下界. 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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1.引言在[1]中,Calabi证明了n+1(n≤4)维Minkowski空间中的完备极大类空超曲面是全测地的。在[2]中 , Cheng-Yau对所有的n证明了这一结论。在[3]中,对于某一类Lorentz流形,Nishikawa证明了类似的结果。并且在[2]中,Cheng-Yau还证明了当具有常数平均曲率的类空超曲面M是Minkowski空间的闭子集时,有 相似文献
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本文给出了非欧氏常曲率空间N^n+1(C)的半平行超曲面的分类,并利用此分类定理证明了非欧氏常曲率空间的高阶平行超曲面与平行超曲面的等价性,从而也给出了非欧氏常曲率空间的高阶平行超曲面的分类; 相似文献
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We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvature of the ambient space is different from zero. As applications, we study umbilical, isoparametric and Einstein null hypersurfaces in Lorentzian space forms and provide several classification results. 相似文献
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We prove that there does not exist any semi-parallel real hypersurface in complex two-plane Grassmannians. With this result, the nonexistence of recurrent real hypersurfaces in complex two-plane Grassmannians can also be proved. 相似文献
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In this paper, we prove that
and round geodesic spheres are the only n-dimensional compact embedded rotation hypersurfaces with Hm = 0 (1 ≤ m ≤ n − 1) in a unit sphere Sn+1(1). When m = 1, our result reduces to the result of T. Otsuki [O1], [O2], Brito and Leite [BL].
The project is supported by the grant No. 10531090 of NSFC. 相似文献
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Some geometrical properties of Hopf hypersurfaces of Kähler manifolds are introduced and a special attention is given to the case of hypersurfaces in complex projective spaces. 相似文献
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The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel. 相似文献