曲率向量

First, the paper introduces the moving coordinate system based on the curve tangent vector and the curvature component vectors. Next, the total curvature vector is composed and the osculating plane determined in the moving coordinate system. The curve bending is then calculated and the recursion analysis made on the osculating plane.

鉴于空间曲线上曲率采集面的变化，引入了由曲线切向量和曲率分量决定的运动坐标系，接着在运动坐标系中合成曲率矢量，确定密切平面，然后在密切平面中对曲线进行弯曲计算和运动坐标系的变换分析，并对相关公式进行了推导。

Chapter 2 introduces some propaedeutics of classic differential geometry, which include the first basic form, the second basic form, normal curvature, main curvature, mean curvature, Gauss curvature, unit normal vector, main vector, etc.

第二章介绍一系列的预备知识，主要是关于古典微分几何中第一，第二基本形式的定义，法曲率，主曲率，平均曲率，Gauss曲率，单位法向量，主方向等的定义。

And obtain that compact submanifolds with parallel mean curvature vector must be totally geodesic.

以及具有平行平均曲率向量的紧致子流形的全测性质。

Triangular mesh, normal vector, principal curvature, gaussian curvature, mean curvature

三角网格，法向量，主曲率，高斯曲率，平均曲率

A pinching theorem of compact pseudoumbilical submanifolds with parallel mean curvature vector in a locally symmetric conformally flat Riemannian manifolds

研究了复空间形式中具有平行法平均曲率向量的紧致全实伪脐子流形。

This pepediscusses compact submanifoldsoftheunit sphere Study is made on conditions ofsubmanifolds with parallel mean curvature vector,submanifolds with flat normal bundle and pseudo-umbilical submanifolds to be umbilical respectively.

本文讨论球的紧致子流形，研究具平行平均曲率向量的，具平坦法丛的、以及伪脐子流形成为全脐子流形的条件，得到几个关于第二基本形式长度千方S的pinching条件。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

First,by choosing a control function for a local adaptive optimal neighborhood,the filter window is set in the region with similar normals to avoid the problem of shrinkage and over-smoothing.

首先通过自适应选取最优邻域控制函数来将滤波窗口限制在顶点法向量相近的区域，以防止滤波后模型的收缩和过光顺；然后运用协方差矩阵分析的方法，在最优邻域内计算出各采样点的法向量和曲率；最后以采样点滤波参考平面为基准，分别平滑采样点的法向量和位置，即先对采样点的法向量进行多边平滑，然后根据新的法向量来多边平滑输出各采样点的位置偏移量，最后在法向方向上移动该顶点，以达到降噪的目的。

In this article,we mainly study the space-like submanifolds with parallel mean curva-ture vector,constant scalar curvature or constant square length of the second fundamental form,respectively.We obtain some pinching theorems and rigidity results by estimating Laplace of the square length of the second fundamental form of the such submanifolds and using yaus maximum principle or Stokes Theorem.

本论文主要研究de Sitter空间中具有平行平均曲率向量、常数量曲率或第二基本形式模长平方是常数的三类类空子流形，并通过分别估计三种情形下子流形的第二基本形式模长平方的Laplace，利用Yau的极大值原理和Stokes定理，获得了这些子流形的一些拼挤定理和刚性定理。

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。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。