查询词典 sphere

Indeed, the reader who is slightly familiar with tessellations of the sphere, the Eaclidean plane and the hyperbolic plane, can easily prove the following result

事实上，稍微熟悉球面、欧几里得平面和双曲平面的分格的读者，都能容易地证明出下面的结果。

In thisthesis, we first extend the vanishing theorem due to Lawson, Simons and Xinto the case of compact submanifolds of a hyperbolic space. Thus, by using thenew vanishing theorem for homology groups, we prove the topological spheretheorem for complete submanifolds in a hyperbolic space. Hence we generalizethe Shiohama-Xu topological sphere theorem.

本文进一步将Lawson-Simons-Xin同调群消没定理拓广到双曲空间中紧致子流形的情形，并运用这一新的同调群消没定理证明了双曲空间中完备子流形的拓扑球面定理，从而推广了Shiohama-Xu的拓扑球面定理。

In this paper, we mainly study the gap of the second fundamental form of hypersurface with constant mean curvature in the unit sphere.

本文主要研究了单位球面内常平均曲率超曲面的第二基本形式模长平方的间隙性。

For Lorentzian hypersurfaces in the Lorentzian sphere, the situation is different from in, the hypersurface may has complex eigenvalues.

对洛伦兹球面S(上标 n+1 下标 1)中的洛伦兹等参超曲面，情况有所不同，可能会有复的特征值。

On the product of unit spheres,we give a kind of natural embeddings from the product unit spheres to the unit sphere in which the product of unit spheres can be viewed as a hypersurface.

第一个是在乘积单位球面上，我们给出自然的由乘积单位球面到高一维球面的嵌入映射，然后考虑了在乘积单位球面上预给定Gauss-Kronecker曲率后，我们所考虑的嵌入的存在性。

In this thesis, we mainly study the relations between compact minimal hypersurfaces of S~(n+1)(1) and the Clifford minimal hypersurface of S~(n+1)(1) by their spectrums, and the relations between unit tangent sphere bundle T_1 M and its base manifold M.

在本文中，我们主要通过谱研究了S~(n+1)(1)中的紧致极小超曲面和S~(n+1)(1)中的Clifford极小超曲面之间的关系，以及单位切球丛T_1M与它的底流形M之间的关系。

Under these coordinate systems, the algorithms that translate hexagonal grid cells from an unfolded icosahedron to a sphere were put forward.

球面离散网格模型是管理海量数据的有效途径，如何构建球面网格是这类模型的基础问题。

In order to generate spherical equal-area grid,this paper finds the corresponding relationships between unfolded icosahedron and sphere using Snyder equal-area projection.

文中利用Snyder等积多面体投影建立了平面与球面的对应关系，设计了球面等积三角形和四边形离散网格的生成算法。

At the same time, by subdividing an icosahedron and projecting all its vertices onto the unit sphere from the center, we can get a spherical triangle mesh with subdivision topology.

然后，将一个正多面体进行细分并将每一次细分所产生的新顶点投影到单位球面上，如此生成一个细分网格。

In the economic sphere, illiberalism usually has to disguise itself through governments trying to adapt it , stressing "capitalism with Chinese characteristics","stakeholder capitalism","fair trade" and so on.

在经济领域，非自由主义通常打着政府试图对全球化进行改造的幌子，强调"中国特色的资本主义"，"混合所有制"，"公平贸易"等等。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。