共查询到20条相似文献,搜索用时 15 毫秒
1.
The authors derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau's results and Ecker-Huisken's results are generalized to higher codimension. In this way, Hildebrandt-Jost-Widman's result for the Bernstein type theorem is improved. 相似文献
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以N表示其截面曲率KN满足a≤KN≤b的n+1维单连通完备黎曼流形,Mn是Nn 1中具有常平均曲率的紧致超曲面,本文给出了这类超曲面关于其第二基本形式模长平方S的积分不等式及相应的刚性定理. 相似文献
3.
Peng Weiling 《Advances in Applied Clifford Algebras》2007,17(2):273-279
The paper discusses the properties of four-dimensional Minkowski space by using Clifford algebra, then gives the concept of
hyperbolic harmonic function by constructing a system (P4) in the four-dimensional Minkowski space, and obtains several properties and a sufficient and necessary condition for the
solvability of the system (P4) . 相似文献
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利用Finsler法曲率A、Landsberg曲率Ly、法切曲率Fy、Berwald联络D以及第二基本形式Ⅱy,研究Minkowski空间中的子流形、子流形的旗曲率与李齐曲率. 相似文献
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In this paper, we study entire spacelike translating solitons in Minkowski space. By constructing convex spacelike solutions to (1.3) in bounded convex domains, we obtain many entire smooth convex strictly spacelike translating solitons by prescribing boundary data at infinity. 相似文献
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本文利用广义的Omori-Yau极大值原则,得到了广义的Robertson-Walker(GRW)时空中具有常高阶平均曲率并且边界包含在一slice中的类空超曲面的高度估计.同时利用这些结果得到了一些拓扑方面的结论.最后对拉普拉斯算子和一些椭圆型的微分算子利用Omori-Yau极大值原则,得到了一些更广泛的非存在性的结果. 相似文献
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For the Monge-Ampere equation det D2u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and the mean curvature of the level sets for the solution to this equation are obtained. 相似文献
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In this paper, we study the relations between a compact spacelike hypersurface with hy-perplanar boundary in the (n 1)- dimensional Minkowski space-time L^n 1 being totally umbilicaland its hyperplanar boundary in a fixed hyperplane π of L^(n 1) being totally umbilical under certainconditions. We give the sufficient conditions for such hypersurface and its hyperplanar boundary tobe totally umbilical in their respective ambients. 相似文献
11.
Luis J. Alías 《Geometriae Dedicata》1999,77(3):297-304
In this paper we establish a sufficient condition for a compact spacelike hypersurface in de Sitter space to be spherical in terms of a pinching condition for the Ricci curvature. Our result will be a consequence of an integral formula involving the Ricci curvature and the scalar curvature of the hypersurface. We also derive some other consequences and applications of this formula. 相似文献
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在Minkowski空间中,定义了定向曲面上的第二类松弛弹性线,推导了在定向曲面上的第二类松弛弹性线的Euler-Lagrange方程.进一步阐明了,这些曲线是否落在曲率线上,最后给出相关的实例. 相似文献
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A Reilly Type Inequality for the First Eigenvalue of Finsler Submanifolds in Minkowski Space 总被引:1,自引:0,他引:1
Bing Ye Wu 《Annals of Global Analysis and Geometry》2006,29(2):95-102
In this paper, we study the extrinsic upper bound for the first eigenvalue of compact Finsler submanifolds in Minkowski space and obtain a Reilly type inequality. It is reduced to the standard Reilly inequality when the ambient space is Euclidean.Mathematics Subject Classification (1991): 53C60, 53B40. 相似文献
14.
双曲虚单位对应一类Minkowski复空间并具有方向异性的特点.四维时空中特殊方向上两时空点间的减法对应类时区与类光区的几何关联,在物理中表示粒子和场的相互作用.通过定义拟(虚)距离使Minkowsk空间的时空映射和间隔不变量进行度量公理化.四维时空中不同方向的距离或度量需要用线度因子和角度因子共同刻画,其中角度因子对应模糊集合,决定了Minkowski度量空间的奇异性质. 相似文献
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研究了三维Minkowski空间中满足ΔG=φ(G+C)条件的类空轴旋转曲面,并给出了该类曲面的分类.主要结论为上述条件中当C为零向量时该曲面拥有常值平均曲率;当C为非零向量时,该曲面或是一类圆锥面、或是二类圆锥面. 相似文献
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研究了Lorentz空间型中具有常数量曲率的紧致类空超曲面,得到了这类超曲面的内蕴刚性定理. 相似文献
17.
G. Santhanam 《Proceedings Mathematical Sciences》2008,118(4):569-572
Let M be a hypersurface in a simply connected space form . We prove some rigidity results for M in terms of lower bounds on the Ricci curvature of the hypersurface M. 相似文献
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研究了三维Minkowski空间E1^3中,类空曲面上曲率线族的切线构成的双曲型直线汇.不仅推广了Abdel-Baky^[1,2]的结论,还进一步研究了此类线汇在E1^3中的其它性质. 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