查询词典 geodesic curvature

By means of moving frame, some properties of ruled surfaces are obtained, including the surfaces being minimal, totally geodesic, totally developableand totally umbilical. Some equivalent conditions in which the ruled surfaces are totally developable are obtained. It is abtained that (k+1)-dimensional ruled surfaces are totally geodesic if and only if they are minimal and totally developable.

利用活动标架法研究了直纹面的一些性质，包括极小性，全可展性，全测地性和全脐性，给出了直纹面是全可展性的一组充要条件，同时得到，R(上标 n+1 下标 v)中的k+1维直纹面M是全测地的充要条件是它是极小的且全可展的。

For any two vertices u and v of a graph G, a u-v geodesic is the shortest path between u and v. The set I consists of all vertices lying on a u-v geodesic. For SV, I is the union of all sets I for vertices u, v∈S. The geodetic number g is the minimum cardinality among the subsets S of V with I=V.

对于图G内的任意两点u和v，u-v测地线是指在u和v之间的最短路。I表示位于一条u-v测地线上所有点的集合，对于SV，I表示所有I的并，这里u，v∈S，G的测地数g是使I=V的最小点集S的基数。

However,there have been no papers which have investigated Minkowski and Minkowski slant helices and Minkowski conical geodesic curves so far as.In this paper,our major study is to give the definition of Minkowski general helix and Minkowski slant helices and Minkowski conical geodesic curves in indicators 1 in pseudo-Euclidean three-space (that is, three-dimensional Minkowski space), and study the definition of equivalence Minkowski general helix, By considering geometric invariants of these space curves, we can estimate the order of contact with those special curves for general space curves.

本篇文章主要研究在指标数为1的3维伪欧氏空间(即三维Minkowski空间)中，我们给出Minkowski一般螺线、Minkowski斜螺线和Minkowski锥面测地线的定义，研究Minkowski一般螺线的等价定义，给出Minkowski斜螺线和Minkowski锥面测地线作为三维Minkowski空间中的特殊曲线所特有的性质，并通过考虑三维Minkowski空间曲线的几何不变量，估计Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和一般Minkowski空间曲线切触的阶数。

This paper presents the explicit expression of geodesic equation on a paraboloids of revolution using differential geometry which avoids the complexity of geodesic ray tracing by numerical approach.

本文根据微分几何原理，从广义费马原理出发，得到了旋转抛物面上短程线的解析式，避免了数值方法射线寻迹的复杂性。

Consider the circle that is tangent to the curve at and has the same curvature there. Its center will lie on the concave side of the curve. This circle is called the circle of curvature. Its radius is the radius of curvature, and

在点处的曲线的法线上，在凹的一侧取一点，使得，以为圆心，半径为的圆叫做曲线在点处的曲率圆，曲率圆的圆心叫做曲线在点处的曲率中心，曲率圆的半径叫做曲线在点处的曲率半径。

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。

On the other hand, Let M~n be an z-dimensional complete noncompactoriented submanifold with finite total curvature in an-dimensional simplyconnected space form F~ of constant curvature c. In this thesis, we provethat if M satisfies one of the following: n≥3, c=0 and integral from n=M H~n＜∞;n≥5, c=-1 and H＜1-2/n~(1/2); n≥3, c=1 and H is bounded, where Hdenotes the mean curvature of M. then the dimension of the space of L~2 harmonic1-forms on M is finite.

本文还证明：若具常曲率c的完备单连通空间型F~中具有有限全曲率的n维完备非紧可定向子流形M满足下面条件之一：n≥3，c=0且integral from n=M H~n＜∞；n≥5，c=-1且H＜1-2/n~(1/2；n≥3，c=1且H有界的，则M上L~2调和1-形式空间的维数是有限的，这里H为M的平均曲率。

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

During the process of model smoothing, there is an uncertain weight threshold, which is discussed in detail for scientific evaluating.2. In the part of "3D Model Segmentation", the vector of Gauss-Mean curvature, that of Max-Min curvature, that of RMS-Absolute curvature are compared through their performances in segmentation.

在三维模型分割方面，对高斯-均值曲率向量、最大-最小曲率向量、RMS-绝对曲率向量等三种特征向量在分割中的性能，以及指定聚类数目对分割结果的影响通过试验进行了比较。

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。

"Bird Man's Diary, Butting on the Love Island", Changsha, China

2008年"鸟人日记，顶在爱情岛"，中国长沙

As long as they were in the service of a family of wizards, their magic would remain dormant.

只要他们一天为家庭服务，他们的法力就潜藏不动。