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1.
A characterization of the Clifford torus   总被引:7,自引:0,他引:7  
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 .

  相似文献

2.
de Sitter空间中具有常均曲率的类空超曲面   总被引:6,自引:0,他引:6       下载免费PDF全文
许志才 《数学学报》1999,42(5):787-794
设M是de Sitter空间中具有常均曲率的类空超曲面,本文给出M是全脐的或是等参的一些条件。  相似文献
3.
Minimizing a differentiable function over a differential manifold   总被引:5,自引:0,他引:5  
To generalize the descent methods of unconstrained optimization to the constrained case, we define intrinsically the gradient field of the objective function on the constraint manifold and analyze descent methods along geodesics, including the gradient projection and reduced gradient methods for special choices of coordinate systems. In particular, we generalize the quasi-Newton methods and establish their superlinear convergence; we show that they only require the updating of a reduced size matrix. In practice, the geodesic search is approximated by a tangent step followed by a constraints restoration or by a simple arc search again followed by a restoration step.A first draft of this paper was first presented at the 10th International Symposium on Mathematical Programming, Montreal, Canada, 1979. The present version has been prepared while the author was visiting the Department of Engineering-Economic Systems at Stanford University, partially supported by AFOSR Grant No. 77-3141.  相似文献
4.
Deformation Theory and The Computation of Zeta Functions   总被引:3,自引:0,他引:3  
We present a new approach to the problem of computing the zetafunction of a hypersurface over a finite field. For a hypersurfacedefined by a polynomial of degree d in n variables over thefield of q elements, one desires an algorithm whose runningtime is a polynomial function of dn log(q). (Here we assumed 2, for otherwise the problem is easy.) The case n = 1 isrelated to univariate polynomial factorisation and is comparativelystraightforward. When n = 2 one is counting points on curves,and the method of Schoof and Pila yields a complexity of , where the function Cd depends exponentiallyon d. For arbitrary n, the theorem of the author and Wan givesa complexity which is a polynomial function of (pdn log(q))n,where p is the characteristic of the field. A complexity estimateof this form can also be achieved for smooth hypersurfaces usingthe method of Kedlaya, although this has only been worked outin full for curves. The new approach we present should yielda complexity which is a small polynomial function of pdn log(q).In this paper, we work this out in full for Artin–Schreierhypersurfaces defined by equations of the form ZpZ= f, where the polynomial f has a diagonal leading form. Themethod utilises a relative p-adic cohomology theory for familiesof hypersurfaces, due in essence to Dwork. As a corollary ofour main theorem, we obtain the following curious result. Letf be a multivariate polynomial with integer coefficients whoseleading form is diagonal. There exists an explicit deterministicalgorithm which takes as input a prime p, outputs the numberof solutions to the congruence equation f = 0 op, and runs in bit operations, for any >0. This improves upon the elementary estimate of bit operations, where n is the number of variables,which can be achieved using Berlekamp's root counting algorithm.2000 Mathematics Subject Classification 11Y99, 11M38, 11T99.  相似文献
5.
本文在Rn+1中定义了一类超曲面并讨论了其上闭测地线长度的下界以及Hamilton系统的周期解的最小周期,这类超曲面比星形超曲面广泛,因而本文结论包含了文献〔1〕、〔2〕、〔3〕中的相应结论  相似文献
6.
LetM n (n>3) be a closed minimal hypersurface with constant scalar curvature in the unit sphereS n+1 (1) andS the square of the length of its second fundamental form. In this paper we prove thatS>n implies estimates of the formS>n+cn−d withc≥1/4. For example, forn>17 andS>n we proveS>n+1/4n which is sharper than a recent result of the authors [5] The second author's research was supported by NNSFC, FECC and CPSF.  相似文献
7.
Lorentz-Minkowski空间中给定主曲率函数的旋转超曲面   总被引:3,自引:0,他引:3  
给出(n,1)型orentz-Minkowski空间中给定主曲率函数的旋转类空超曲面的位置向量场,通过计算超曲面的主曲率,证明了这类超曲面的存在性.  相似文献
8.
关于高维Willmore问题   总被引:3,自引:0,他引:3       下载免费PDF全文
马志圣 《数学学报》1999,42(6):0-1046
本文考虑高维欧氏空间中子流形M的一组有较好意义的共形不变的泛函。给出这些泛函通过M的Betti数的下界估计;给出对于管状超曲面的下界和对于双球环的下界以及达到这些下界的相应的子流形,并且证明对于管状超曲面所得的有关Betti数的下界是不精确的,方法是不适当的,给出类似Willmore猜测的一些猜测。  相似文献
9.
A Parametrization of Isometric Immersions between Hyperbolic Spaces   总被引:2,自引:0,他引:2  
We parametrize the space of isometric immersions of the hyperbolic n -space into the hyperbolic ( n +1)-space by a family of properly chosen (at most) countable n -tuples of real-valued functions. This is an answer to the problem posed by Nomizu in 1973. We also construct a one-parameter family of deformable isometric immersions from the quotient spaces of the hyperbolic 2-plane modulo and some totally discontinuous subgroups of isometries.  相似文献
10.
局部对称黎曼流形中的超曲面   总被引:2,自引:0,他引:2  
研究了局部对称黎曼流形中具有常平均曲率超曲面的几何性质,得到了关于其第二基本形式模长平方的拼挤定理.  相似文献
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