共查询到18条相似文献,搜索用时 62 毫秒
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本文研究了复射影空间中具有常数量曲率的完备全实子流形的问题.利用丘成桐的广义极大值原理和自伴随算子,获得了这类子流形的某些内蕴刚性定理. 相似文献
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de Sitter空间中具有常数量曲率的完备类空子流形的间隙现象 总被引:1,自引:0,他引:1
设Mn是de Sitter空间Snp p(c)中具有常数量曲率R(≤c)的完备类空子流形.得到了Mn关于其第二基本形式模长平方‖h‖2的间隙性定理,如果n(c-R)≤‖h‖2≤2√n-1c,那么,或者‖h‖2=n(c-R)且Mn是全脐点子流形,或者‖h‖2=2√n-1c且Mn是全脐的或是双曲柱面Sn-1(c-tanh2r)×H1(c-coth2r). 相似文献
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本文研究了双曲空间Hn+1(-1)中具有常数量曲率的完备超曲面.利用活动标架的方法,得到此类超曲面的两个刚性定理. 相似文献
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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
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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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Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau's self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms. 相似文献
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该文研究了局部对称共形平坦空间中具有常数量曲率的紧致子流形,证明了这类子流形的某些内蕴刚性定理. 相似文献
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本文利用一个类似于Cheng和Yau引进的微分算子的新微分算子,得到了单位球面中常数量率的紧致子流形的一个刚性结果. 相似文献
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CompleteSpace-likeSubmanifoldsinadeSitterSpacewithParallelMeanCurvatureVectorShuShichang(XianyangTeachersCollege,Xianyang,712... 相似文献
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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
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In this paper we show how to embed a time slice of the Schwarzchild spacetime that models the outer space around a massive star, as a Lagrangian submanifold invariant under the standard action of the special orthogonal group on complex Euclidean space. This result is generalized for rotationally invariant metrics that can be considered as higher-dimensional versions of Schwarzchild's and these submanifolds are locally characterized as the only ones with zero scalar curvature inside the above family. 相似文献
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In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively. 相似文献
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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
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本文证明了de Sitter空间中具平行平均曲率向量的完备类空子流形在其第二基本形式模长平方S<2(n-1c)的平方根时是全脐子流形。 相似文献