1) sectional curvature
截曲率
1.
This paper uses the important equation∫DF|du|22g(X,n)σg=∫DF′|du|22h(uX,un)σg+∫D(divSF(u))(X)vg+∫D〈SF(u),X〉vg to discuss the constant boundary-valued problems for exponential-harmonic maps on complete simply connected Riemannian manifolds with negative sectional curvature, and obtains Liouville-type theorems.
应用重要等式∫DF|d2u|2g(X,n)σg=∫DF′|d2u|2h(uX,un)σg+∫D(divSF(u))(X)vg+∫D〈SF(u),X〉vg,讨论完备单连通具有负截曲率黎曼流形上指数调和映照的常边值问题,得到相应的刘维尔型定理。
2.
Some results on inherent rigidity for compact minimal submanifolds in a sphere are given,and the Pinching constants with respect to the sectional curvature and the Ricci curvature in S.
给出球面上紧致极小子流形的某些内蕴刚性定理,改进了丘成桐、沈一兵等人关于截曲率和Ric ci曲率的Pinching常数。
3.
The paper partially solves the problem on the condition of the manifold with Ric M- > 0 or its sectional curvature bounded below.
Ｗｕ在［４］中提出这样的问题：若一完备非紧的黎曼流形仅有两个符号相反的Ｂｕｓｅｍａｎｎ函数，则该流形的结构如何？本文在流形具非负Ｒｉｃｃｉ曲率或截曲率具下界的情况下部分地解决了这一问题。
2) sectional curvature
截面曲率
1.
On pinching problem of sectional curvature on minimal submanifolds in a symmetric space;
局部对称黎曼流形中极小子流形的截面曲率的pinching问题
2.
Let Mmbe a compact submanifold with positive sectional curvature of a space form Nn(c).
设Mm是空间形式Nn(c)中具有正截面曲率的紧致子流形,证明了如果n-m≥2,Mm的平均曲率向量关于法联络平行且不为零,则在Mm中不存在稳定积分流,且Mm的同调群消没。
3.
By using an inequality relation between a scalar curvature and the length of the second fundamental form,it is proved that sectional curvatures of a submanifold must be nonnegative (or positive).
利用数量曲率与第二基本形式长度之间的一个不等式关系,证明了其子流形的截面曲率一定非负(或者为正),并将此应用到紧致子流形上,得到一些结果。
3) cross section curvatures
截现曲率
4) φ-sectional curveture
φ-截曲率
5) holomorphic bisectional curvature
双截曲率
6) radial sectional curvature
径向截曲率
1.
If the absolute value of the radial sectional curvatures satisfies some conditions on M - S , σ（－△）＝σess（－△）＝［o，∞）.
如果M的径向截曲率在M－S上，其绝对值满足一定条件，那么σ（－△）＝σess（－△）＝［0，∞）。
补充资料：截面曲率
截面曲率
sectional curvature
截面曲率汇，犯柱佣目~撅;ee料。o。”曲冲加朋3.a]，亦称截曲率 可微R正仃以nn流形M在一点p沿一个二维平面“的方向(沿在P任M确定“的二重向量的方向)的RIOm.”n曲率(Rlenlannlan cun忍tLu℃). JI .A.C朋opoa撰[补注]
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条