截面曲率

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。

The complete pseudo-umbilical submanifolds with parallel mean curvature vector in constant curvature space;2. In this paper,the pseudo-umbilical submanifolds with parallel mean curvature vector in pseudo-Riemannian manifold is discussed.

研究了伪黎曼流形中具有平行平均曲率向量的伪脐子流形，Npn+p为n+p维完备连通伪黎曼流形，它的截面曲率KN满足a≤KN≤b，Mn为Npn+p中紧致的具有平行平均曲率向量的伪脐子流形。

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。

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。

C arbitrarily inequiaxial T-shaped, L-shaped and "十"shaped columns subjected to 792 load conditions is calculated using compiled C++ programme. On the basis of calculation results, the factors influencing the worst load orientation are analyzed and load orientation of the least curvature ductility of three kinds of sections is presented.Furthermore a analysis of failure mechanism for R.

本文采用非线性全过程分析方法，采用C++语言编制了不等肢异形柱截面曲率延性比的计算程序，首先计算了不等肢T形、L形和十字形柱在792种工况下的截面曲率延性比，在此基础上分析了影响不等肢异形柱截面延性的最不利荷载方向的各种因素，并得出了这三种截面不等肢异形柱在上述工况下的截面延性最不利荷载方向。

In this paper, we consider the n-dimensional hypersurfaces (n≥3) with vanishing Mbius form Φ.

本文考虑了S(上标 n+1)(n≥3)中具有消失Mbius形式Φ的超曲面：对具有调和曲率张量的超曲面进行分类，进而，在Mbius度量的意义下，对Einstein超曲面和具有常截面曲率的超曲面也进行了分类。

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％。