Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

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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.

第二章介紹一系列的預(yù)備知識，主要是關(guān)于古典微分幾何中第一女教师日韩精品视频，第二基本形式的定義黄网站色视频，法曲率91久久婷婷人人澡人人澡，主曲率黑人欧美视频巨粗巨大巨硬，平均曲率国产城中村自拍，Gauss曲率，單位法向量黄色网站免费提供免费服务，主方向等的定義中国国产精品无码理论片。

Like the F-22, the Lamborghini Reventon is a fusion of Positional and Curvature form development, but its origami-like folding of sleek surfaces signies a threatening yet exotic precision; a technological sex appeal that cuts both ways.

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A new curvature-based algorithm in free-form curve fitting was proposed to fit a 2D NURBS profile with an arc spline ,where a new form of curvature formula with matrix representation was also proposed,and then the arc spline tool path with G~(1) continuity was generated.

給出了一種平面曲線輪廓的圓弧樣條擬合及刀具路徑生成算法人人操人人人看，該算法面向零件輪廓的光順性刀具路徑生成，通過應(yīng)用曲線的曲率關(guān)系十八岁不能看的黄色网站，對以NURBS表示的被擬合自由曲線按參數(shù)遞增的方向用G1連續(xù)的圓弧或直線段逐段擬合日韩无码高清啪啪啪高潮，并生成相應(yīng)的圓弧樣條刀具路徑，從而實(shí)現(xiàn)零件曲線輪廓表面的光順加工欧美操女视频。

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.

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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.

本文還證明：若具常曲率c的完備單連通空間型F~中具有有限全曲率的n維完備非緊可定向子流形M滿足下面條件之一：n≥3欧美影院成年免费版视频在线播放，c=0且integral from n=M H~n＜∞；n≥599热在线观看精品免费，c=-1且H＜1-2/n~(1/2久久精品人妻无码一区二区三区；n≥3，c=1且H有界的性无码在区，則M上L~2調(diào)和1-形式空間的維數(shù)是有限的欧美日韩黄色三级久久，這里H為M的平均曲率。

Methods:According to the standard of Borden Ways and Seze Ways to measure the regular cervical and lumbar curvature, then use the sectorial area formula of mathematics geometry to calculate the regular curvature arch form area of cervical and lumbar.

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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.

對NURBS曲面的曲率線的積分進(jìn)行了系統(tǒng)的公式推導(dǎo)，并利用NURBS曲面的離散法向量有效地簡化了曲面第二基本量的計(jì)算蜜芽tv国产精品一级毛片，加速了Euler法迭代求解曲率線微分方程的過程色色亚洲色；在求得曲率線上的離散點(diǎn)集以后，應(yīng)用奇異混合插值技術(shù)特级毛片高潮一级一级毛，在可控精度內(nèi)把曲率線用顯式直接表示為位于NURBS曲面上的B樣條曲線国产精品一线天在线观看。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高復(fù)雜曲面多坐標(biāo)數(shù)控加工精度和加工效率為目的，在對國內(nèi)外研究現(xiàn)狀進(jìn)行深入分析的基礎(chǔ)上91精品自产拍不卡，對數(shù)控編程中各環(huán)節(jié)的關(guān)鍵技術(shù)問題進(jìn)行了深入研究qq午夜6080，主要內(nèi)容包括以下幾方面： 1 分析了復(fù)雜曲面各種造型方法的優(yōu)缺點(diǎn)，給出了根據(jù)各種邊界條件所確定自由曲面的NURBS表示方法以及三次NURBS曲線曲面反算算法一级黄色片日日爱；用微分幾何理論推導(dǎo)了NURBS曲面的偏導(dǎo)矢及法曲率計(jì)算表達(dá)式日韩毛片无码一级观看；對曲面不同曲率特性區(qū)域的幾何特征進(jìn)行了深入分析，為建立復(fù)雜曲面的數(shù)控加工刀位計(jì)算模型奠定了理論基礎(chǔ)色黄乱婬伦免费网站耙。

Using the mathematical tool"DifferenceGeometry",it is possible to define the discrete geometric metrics such as discretefirst fundamental form,discrete second fundamental form,discrete unit mainnormal vector,discrete Gauss curvature,discrete mean curvature and discreteLaplacian.

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