高斯曲率

On the other hand,the conformal deformations problem is to find a metric on H2(-1), conformal to g,with the given function K as its Gaussian curvature ,that is,it is important for us to study the solvability of the conformal Gauss curvature equation in geometry analysis.

e~(2u)g，它的高斯曲率函数K满足共形高斯曲率方程Δ_gu+1+Ke~(2u)=0。另一方面，对H~2(-1)上预先给定的一个函数K，共形形变问题-寻找g的共形度量=e~(2u)g使K是的高斯曲率，即共形高斯曲率方程的可解性研究是几何分析中的一个重要问题。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

In this paper, we mainly discuss a kind of surfaces in4- dimensional Pseudo-Euclidean Space and give the classification of such surfaces with constant mean curvature and Gauss curvature.

文章研究四维伪欧氏空间中的一类曲面，给出了具有常平均曲率、高斯曲率及相关平均曲率和高斯曲率的这类曲面的分类。

But it operates on the triangle mesh of 3-D objects surface retrieved from range images, and calculates the value and sign of Gauss curvature according to the geometrical meaning of Gauss curvature in differential geometry, which merits are its accuracy and speed.

该方法在理论上没有从拟合表面、求表面偏导的传统思路出发，它使用从深度图像得到的三维物体表面的格网表示，直接根据高斯曲率的几何意义计算高斯曲率的大小和符号。

Emphases are put on solving the problem of repeating searching extreme points in contours of Gauss curvature drawing,and the improved Bulirsch Stoer contour curve searching method is used in extreme points searching to speed up the searching efficiency.

提出了一种针对非均匀有理 B样条自由曲面的高斯曲率等值线的光顺检测方法，重点解决绘制高斯曲率等值线时出现的极值点的重复搜索问题，并将改进的Bulirsch-Stoer等值线搜索法用于极值搜索中，提高了搜索效率。

Then, the first and second fundamental forms, Gaussian curvature and mean curvature of the surfaces are directly calculated according to the principles of differential geometry.

首先，根据微分几何中的基本知识，得到了该种度量形式下的平移曲面的第一、第二基本形式以及高斯曲率和平均曲率；然后，主要利用高斯曲率和平均曲率之间的线性关系和平方关系，得到了这类平移曲面的分类定理。

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

The approach of solving mean curvature,Gaussian curvature and principal curvatures of general triangular mesh model was derived.Considering coarse triangular mesh model is often seen,in order to increase the precision of curvatures,combined with Loop subdivision algorithm,the curvature algorithm was further extended.

推导了一般三角形网格模型顶点的平均曲率、高斯曲率和主曲率的计算方法，考虑到经常遇到粗糙三角形网格模型，为提高其曲率计算方法的精度，结合Loop细分曲面算法，进一步拓展了该曲率计算方法。

Considering coarse triangularmesh model is often seen, in order to increase the p recision of curvatures,combined with Loop subdivision algorithm, the curvature algorithm was further extended.

推导了一般三角形网格模型顶点的平均曲率、高斯曲率和主曲率的计算方法，考虑到经常遇到粗糙三角形网格模型，为提高其曲率计算方法的精度，结合Loop 细分曲面算法，进一步拓展了该曲率计算方法。

Its implementation processes include:①to perform wavelet transform and frequency decomposition and reconstruction to gain the seismic data with high quality;②to adopt least square method to approach and fit the local secondary curved face, and compute the fit coefficients of the secondary curved face, then use these coefficients to gridding mapping bed plane to compute the average curvature and Gauss curvature, then, obtain other curvatures through the various linear combinations of the two curvatures above;③to generalize the curvature of the bed layer to compute and reconstruct the curvature volume.

其实现过程为：①对地震资料进行小波变换、分频重构，获得高质量的地震资料；②采用最小二乘法一次逼近，对局部二次曲面进行拟合，求取二次曲面拟合系数，并利用这些系数对网格化成图层面计算平均曲率和高斯曲率，再从两个曲率的不同线性组合，获取其他曲率；③将层面曲率推广，计算和重构曲率数据体。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。