查询词典 submanifold

Some uniform formulae are established, which link the Laplacian of the position vector function to the mean curvature vector field on any submanifold in the space forms.

讨论空间型中的位置向量场，建立一组统一的公式，将子流形的平均曲率向量场与位置向量及其衍生函数的Laplacian联系在一起。

Then M is a hypersurface of a (n +1)-dimensional totally geodesic submanifold Sn+1 of Sn+p .

则M是S~的一个(n+1)-维全测地子流形S~(n+1)中的超曲面。

An isometric immersed submanifold which receives the least possible amount of tension from the surrounding space at each point is called an ideal immersion.

当一个浸入子流形在每一点处接受来自于外围空间的最小张力时，这种浸入称为理想浸入。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simon\'s nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simons nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Theorem 2 Let M~n be a compact totally real minimal submanifold in M~n which is a locally symmetric Bochner-Kaehler manifold.If the infimum of sectional curvature R_c in M~n satisfies: then M~n must be totally geodesic in M~n.

定理2 M~n是局部对称Bochner-Kaehler流形M~n中紧致全实极小子流形，如果M~n截面曲率下确界R_c满足：则M~n必是全测地的。

Using Lagrangian submanifold in symplectic space ,we give a complete discription and classification of the self-adjoint domains of the 2-nd order and high order singular differential operators on infinite interval .

给出了与微分算子自共轭域相对应的Lagrangian子流形的描述和分类情况。

While the new components having the same numbers with these original physical vectors are introduced and the new components are combined with those original physical components to form a new symplectic space, the ray problem of wave propagation in geometrical optics is converted into the problem of Lagrange submanifold in the symplectic space.

本论文的工作作为国家自然科学基金地震波传播与成像项目（NO.40174032）的一部分，得到如下结果：论文分析了利用Maslov方法求解非均匀介质中波动方程高频近似解的基本原理和求解过程，构造了介质系数只在一个方向变化时波动方程高频近似解的通用计算公式。

Let M be a compact submanifold of locally symmetric space N~,we apply Gauss equation,Ricci equation and the property of locally symmetry of the outer space ,through studying f =.

我们应用Gauss方程，Ricci方程和外围空间的局部对称性质等方法，通过研究函数f=？

In this paper, we discuss the 2-harmonic spacelike submanifolds in a locally symmetric and conformally flat pseudo-riemannian manifold and get two sufficient conditions under which Mn turns into a maximal submanifold,and the results in [2] are improved.

讨论局部对称共形平坦伪黎曼流形的2-调和类空子流形，得到这类子流形成为极大的二个充分条件，推广了文[2]中的结论。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐