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本文的主要结果是:Lorentz-Minkowski空间中介于两个同心伪圆柱面之间的完备、类空、常平均曲率超曲面必为伪圆柱面,即乘积空间R~k×H~(n-k).对于常高阶平均曲率的情况,如果截曲率有下界,那么介于两个同心伪球面之间的完备类空超曲面必为伪球面. 相似文献
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本文的主要结果是:Lorentz-Minkowski空间中介于两个同心伪圆柱面之间的完备、类空、常平均曲率超曲面必为伪圆柱面,即乘积空间R~k×H~(n-k).对于常高阶平均曲率的情况,如果截曲率有下界,那么介于两个同心伪球面之间的完备类空超曲面必为伪球面. 相似文献
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本文考虑三维 Euclid 空间 R~3中拓扑型为球面的有限全曲率完备嵌入极小曲面.通过对伪嵌入极小曲面的研究,证明了一类嵌入极小曲面的不存在性,并明确了伪嵌入与嵌入极小曲面的差异. 相似文献
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我们研究四维球面中的1-极小稳定完备非紧超曲面.得到在适当限制平均曲率与高斯曲率的情况下,四维球面中不存在具有多项式体积增长的1-极小稳定完备非紧超曲面.这些结果部分证实了外围空间是四维球面时Alencar等人提出的猜测. 相似文献
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本文把Berard P.,do Carmo M.,Santos W.在1998年所得的结果,分别推广到局部对称的Cartan-Hadamard流形中具有常平均曲率和有限全曲率的完备超曲面,以及球面上具有平行平均曲率和有限全曲率的完备子流形. 相似文献
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林森春 《数学年刊A辑(中文版)》1989,(3)
本文首先讨论纯量曲率R和平均曲率H满足R=kH,k=Const。的完备曲面帮超曲面。证得:R~3中这样的曲面是球面、柱面或平面;R~(n 1)中这样的超曲面当它是凸的且R有上界时是超球面、超平面或广义圆柱面;R~(2 p)(p≥1)中这样的曲面在一定附加条件下是包括球面和平面在内的四种曲面,最后讨论类似的子流形。这些结果改进或推广了[5,6,7]的结果。 相似文献
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设F(t)是上伪球面H_+~n上时轴旋转不变且满足凸条件的光滑函数.本文证得:Lorentz空间L~(n+1)中,以圆球面S~(n-1)(R)为边界且有非零常F-平均曲率的紧致类空超曲面必为Wulff帽. 相似文献
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本文研究伪黎曼空间型中一类特殊的Weingarten超曲面的存在性问题.通过引入伪黎曼空间型中旋转超曲面的概念,并给出其主曲率计算公式.得到伪黎曼空间型中旋转型Weingarten超曲面的存在性定理.推广并统一了相关结果. 相似文献
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M. Zippin 《Israel Journal of Mathematics》1975,22(2):110-117
It is proved that every subspace ofl 1 which is an Λ1, λ space with λ close enough to 1 is isomorphic tol 1. 相似文献
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We show that a broad class of extensions of measure preserving systems in the context of ergodic theory can be realized by
topological models for which the extension is “almost one-one”. 相似文献
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V. F. Babenko 《Ukrainian Mathematical Journal》1994,46(10):1557-1560
We obtain the exact values of the bestL
1-approximations of the classesW
1
r
of periodic functions by periodic polynomial splines of degreer and defect 1 with equidistant knots that belong to the classW
1
r
.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1410–1413, October, 1994. 相似文献
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A.P. Markeyev 《Journal of Applied Mathematics and Mechanics》2012,76(1):36-47
The motion of a satellite about its centre of mass in a central Newtonian gravitational field is investigated. The satellite is considered to be a dynamically symmetrical rigid body. It is assumed that the ratio of the polar and equatorial principal central moments of inertia of the satellite is 4/3, or close to this. The orbit of the centre of mass is elliptic, and the orbit eccentricity is assumed to be small. In the limit case, when the orbit of the centre of mass is circular, a steady motion exists (corresponding to relative equilibrium of the satellite in the orbital system of coordinates) in which the axis of dynamic symmetry is directed along the velocity vector of the centre of mass of the satellite; here, the frequencies of the small linear oscillations of the axis of symmetry are equal or close to one another. But in an elliptic orbit of small eccentricity, multiple 1:1:1 resonance occurs in this case, as the oscillation frequencies mentioned are equal or close to the frequency of motion of the centre of mass of the satellite in orbit. The non-linear problem of the existence, bifurcations and stability of periodic motions of the satellite with a period equal to the rotation period of its centre of mass in orbit is investigated. 相似文献
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关于Goormaghtigh方程(x~3-1)/(x-1)=(y~n-1)/(y-1) 总被引:3,自引:0,他引:3
本文证明了:Goormaghtigh方程适合的例外解(x,y,n),满足以及 相似文献