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单词 Second fundamental form
释义

Second fundamental form

中文百科

第二基本形式

微分几何中,第二基本形式second fundamental form)是三维欧几里得空间中一个光滑曲面的切丛上一个二次形式,通常记作 II。与第一基本形式一起,他们可定义曲面的外部不变量,主曲率。更一般地,若在黎曼流形中一个光滑超曲面上选取了一个光滑单位法矢量场,则可定义这样一个二形式。

英语百科

Second fundamental form 第二基本形式

Definition of second fundamental form

In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional Euclidean space, usually denoted by \mathrm{I\!I} (read "two"). Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is defined for a smooth hypersurface in a Riemannian manifold and a smooth choice of the unit normal vector at each point.

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