查询词典 sectional curvature

Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

基础科学，数学，几何、拓扑Hausdorff收敛；几乎非负Ricci曲率；贝蒂数；调和1-形式；幂零指标；分裂定理；正截面曲率；梯度曲线

If we give some restrician to the intrinsic quantities of submanifolds, such as second fundamental form, scalar curvature,Ricci curvature or sectional curvature,then we can get some new property of the submanifolds.The procedure is called pinching problem of submanifolds.

对子流形的第二基本形式模长平方s，数量曲率R，Ricci曲率R_及截面曲率R_等内在量，加以某种限制，从而得到子流形的某些性质，叫做子流形的pinching问题。

The Pinching problems are discussed on the sectional curvature of compact space-like pseudo-umbilical submanifolds M~n with parallel mean curvature vector in De Sitter space S~_p, and the theory of reduction of the codimension is obtained in De Sitter space through evaluating the Laplacian of square of the length.

讨论了De Sitter空间Snp+p中，具有平行平均曲率向量的紧致类空伪脐子流形Mn的截面曲率的拼挤问题，通过估计第二基本形式模长平方的Laplacian，得到了De Sitter空间中的余维数压缩定理。

Given a hyperbolic plane H2(-1)=,whose sectional curvature k is function K is the Gaussian curvature of the conformal metric g = e2ug ,then K satisfies the conformal Gauss curvature equation .

设H~2(-1)=是具常截面曲率k==1的双曲平面，其中B={∈R~2：x~2+y~2＜1}是单位圆盘，g=4(dx~2+dy~2)/(1-x~2-y~2)~2是所谓的Poincaré度量。考虑H~2(-1)上的共形形变度量？

If the infimum of sectional curvature R_c in M~n satisfies: then M~n must be totally geodesic in M~,T_c is the supremum of Ricci curvature and t_c is the infimum of Ricci curvature in M~

如果M~n的截面曲率下确界R_c满足：则M~n一定是全测地的其中T_c，t_c分别是M~(n+p上Ricci曲率上确界和下确界。

We get some results about the scalar curvature of 2 and n(n≥3)dimensions Einstein manifold :ρ Maybe is constant and ρ is constant, the relation between Einstein Manifold and Riemannian Manifold with constant sectional curvature.

本文对其有关性质进行了讨论，得到了2维和n(n≥3)维爱因斯坦流形的数曲率的一些结果：ρ可能为常数和ρ为常数，以及爱因斯坦流形与常曲率黎曼流形之间的关系

In chapter 4,we consider the existence of harmonic function in negative sectional curvature manifolds.we get that,if Ricci ≥-C(1 + r~2)r =ρ(O.x, then there have non-canstant bounded harmnic function in negative sectional curvature manifolds.

第四章考虑负曲率流形上调和函数，得到了在Ricci≥-C(1+r~2)其中r=ρ的负曲率流形的调和函数的存在性。

Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.

定理4局部对称Bochner-Kaehler流形中不存在具有非零平行平均曲率向量且截面曲率大于零的紧致全实2-调和子流形。

Its amount has relation with acting load. The influence on sectional curvature of bending components is the greatest one, the ultimate curvature of corroding section decrease obviously, and the sectional curvature increases rather sharply with the increase of rust rate during the process of corrosion. The anti-cracking capacity of prestressed bending R. C. components may be damage. For the convenience of engineering usage and damage evaluation of structure, this paper presents a concept of sectional damage coefficient on the foundation of experimental and treatment study.

试验与理论研究均表明，受压区钢筋锈蚀后对普通钢筋混凝土和预应力钢筋混凝土受弯构件的承载力影响均不大，但对构件的正常使用性能有较显著的影响，受压区钢筋锈蚀过程中，截面刚度有较显著的下降，挠度及受压区混凝土压应变随锈蚀量增加而增加，增加值与使用荷载大小有关；受弯构件的截面曲率所受影响最大，锈蚀后截面的极限曲率有明显的下降，在使用荷载作用下，截面曲率则随钢筋锈蚀量的增加而有较显著的增加；而预应力混凝土受弯构件的抗裂度会下降。

Theorem 3 Let M~n be a compact totally real 2-harmonic submanifold in M~n which is a locally symmetric Bochner-Kaehler manifold.If Ricci curvature of M~n is nonegative and positive at a point at least,then the holomorphic sectional curvature of M~n is a postive constant number.

定理3设M~n是局部对称Bochner-Kaehler流形M~n的紧致全实2-调和子流形，若M~n的Ricci曲率非负且至少在一点为正，则M~n具有正常数全纯截面曲率。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。