脐点

设M是单位球面上不含脐点的子流形，Moebius形式Φ消失，本文讨论M关于Mobius度量的截曲率的Pinching问题。

Let M be a submanifold without umbilic point on unit sphere ; its Moebius form Φ vanishes , in this paper the pinching theorems of sectional curvature about Moebius metric are obtained .

脐点：是淀粉粒的形成中心，淀粉成层积聚在脐点周围。

The center of a starch grain around which the layers of starch are deposited .

强震危险地点的判定及强震预测&利用椭圆脐点突变模式

Judgement of strong earthquake hazard area and prediction of strong earthquake ── by elliptic umbilic catastrophe model

文章利用脐点的性质研究了二次曲面的圆截口问题，并给出了与二次曲面交线为圆的圆截口的方程的一种求法。

In this paper , we make use of the properties of the umbilic to research circle Section question of quadric in3-dimensional euclidean space .

设M~n为（n+1）维单位球面S~（n+1）中的无脐点超曲面。根据王长平教授的M（？）

Let M ~ n be an immersed umbilic-free hypersurface in ( n + 1 ) - dimensional unit sphere S ~ ( n + 1 ) .

中的孤立脐点的性质进行研究，得出Q~3。

At last by studying the property of isolated umbilic point in Q ~ 3 , the umbilic points index sum theory of positive definite oriented closed surfaces in Q ~ 3 is discovered .

本文论证了全脐点曲面必为球面或平面，并讨论了球面曲线的一系列性质，揭示了这类曲线的曲率和挠率之间的特殊关系，从而刻画出其几何特征。

The author proves whole omphalion curved surface is surely a spherical surface or plane , and discusses a series of properties of the curve on spherical surface , revealing the special relation between curvature and torsion rate of this kind of curve to depict its geometric features .

并且证明了：若R>1，则M是全脐的或者是无脐点的。

It also shows that M is either totally umbilic al or else umbilic free , if R > 1 .