In this paper, we give explicit constructions and formulations for harmonic maps from R1,1 into classical real semisimple Lie groups by using Darboux transformation. We also discuss pluriharmonic maps from complex manifoldsinto symmetric spaces and Willmore surfaces in Sn. By converting geometric conditions satisfied by these maps into integrable systems, and using the the-ory of integrable systems, we give explicit constructions for pluriharmonic maps from complex manifolds into symmetric spaces and the Willmore surfaces in Sn respectively. Finally, we classify hypersurfaces in Sn+1 with three distinct prin-ciple curvatures and zero Mobius form using the theory of Mobius geometry. The paper consists of four chapters.

本文首先利用Darboux變換的方法給出了從Lorentz平面R~(1360天天色秋霞，1)到經(jīng)典實半單Lie群的調(diào)和映照的具體構(gòu)造，并給出其顯式表示国产一级精品毛片視屏；其次研究了復(fù)流形到對稱空間的多重調(diào)和映照及球空間S~n中Willmore曲面可以直接免费观看的av毛片，將這些映照所滿足的幾何條件轉(zhuǎn)化為可積系統(tǒng)，然后利用可積系統(tǒng)理論分別給出復(fù)流形到對稱空間的多重調(diào)和映照與S~n中Willmore曲面的構(gòu)造中国一级A片XXXX；最后利用Mōbius幾何的理論給出S~(n+1)中具有三個不同主曲率且Mōbius形式為零的超曲面的分類又粗又硬一级A片。

For the Ricci flow on n-dimensional (n ≥ 4) manifolds, if the initial metric possess positive curvature operator and strong pinching conditions, then we can get the similiar results, consult the reference papers , and .

對于維數(shù)n≥4的黎曼流形，如果初始的度量的正曲率算子加上足夠強的拼擠條件能看av的网站，也能夠得到類似的結(jié)果黄色视频三级片真人，參見[Hu1]，和免费看av的在线网站。

Next in section 2.3,usingthe finite isolated regular representations in SO(3)character varity of 〓,weobtained a computation formula of SO(3)Donaldson invariants with degree 1 of4—manifold 〓(Theorem 2.3.1).Finally in section 2.4 wediscussed the Donaldson invariants of 4—manifolds with smoothly embedded 2—torus 〓 whose selfintersection is +1,with the help of the single irreducibleSU(2)representation of the principal 〓—bundle over a 2—torus with Eulernumber—1,we got a gluing formula of the Donaldson invariant on the 2—homology represented by 2—torus 〓(Theorem 2.4.1),it is a supplement of P.

最后在§2.4我們討論了具有自交數(shù)為+1的嵌入環(huán)面〓的4—流形的Donladson不變量天天狠天天透天干天天xa55，運用環(huán)面上歐拉數(shù)為-1的圓叢的單個不可約SU（2）表示給出了Donaldson不變量在環(huán)面表示的同調(diào)類上的一個粘合公式（定理2.4.1），這一結(jié)果補充了P。

In chapter 2 we recall the basic facts about Riemannian manifold and some notions of the transform theory on Riemannian manifolds.

首先成年人AV网站，利用給定流形的向量叢上聯(lián)絡(luò)的存在性給出流形上的不可積分布上非完整聯(lián)絡(luò)的存在性證明日韩激情中文字幕视频在线，進而證明了次黎曼聯(lián)絡(luò)的存在唯一性，并以此為出發(fā)點研究了次黎曼流形中仿射變換a片免費大全、等距變換91日韩在线视频免费观看、共形變換和射影變換下的一些不變性質(zhì)，給出了相應(yīng)變換下的一些不變量求一级黄色网站。

In this paper,focusing on the symplectic manifolds,we discuss the Seiberg-Witteninvariants,some basic construction.the existence of symplectic forms,and the existenceof Riemannian metric of positive scalar curvature.

本文主要圍繞辛流形欧美湿身诱惑超碰在线，討論其Seiberg-WItten不變量、辛流形的一些基本構(gòu)造很黄很色很污的免费网站，辛形式的存在懷及其上是否存在具有正數(shù)量曲率的黎曼度量等問題而展開的网站在线观看无码天堂。

Its main goal is to explore information relating to the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other important problems such as the Novikov conjecture, the Baum-Connes conjucture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature and so on.

其主要目標是通過幾何空間（如非緊完備黎曼流形、有限生成群等）大尺度幾何結(jié)構(gòu)的信息中文字幕在线免费观看网址，建立幾何空間的幾何免费观看国产黄网站在线、拓撲與分析之間的聯(lián)系，并應(yīng)用于解決其他重要問題黄网站在线视频观看，如Novikov猜測www.2014av、Baum-Connes猜測， Gromov-Lawson-Rosenberg正標量曲率猜測等欧美XXXXX高潮在线观看。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗幾何上的指標理論是"非交換幾何"領(lǐng)域九十年代以來發(fā)展起來的重要研究方向色色色色色色色色五，它孕育于非緊流形上的指標理論，其主要目標是通過幾何空間（如非緊完備黎曼流形日韩AV操逼、有限生成群等）的大尺度幾何結(jié)構(gòu)探索指標代數(shù)一级三级片免费视频，即 Roe代數(shù)，的K-理論群的信息一区二区亚洲，從而建立幾何空間的幾何18紧网站、拓撲與分析之間的聯(lián)系，并應(yīng)用于解決其他重要問題欧美在线亚洲一区二区欧美，如Novikov猜測无遮无码免费裸交视频暖暖、Gromov-Lawson-Rosenberg正標量曲率猜測、群C*-代數(shù)冪等元問題等久久精品9999热。

The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.

對于黎曼流形的浸沒建立了垂直能量泛函的二階變分公式精精国产XXXX视频在线my，研究強垂直調(diào)和映射的穩(wěn)定性。

Fundamental concepts in power system differential-algebraic equations model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied.

所得研究成果揭示了微分代數(shù)模型與奇異擾動模型的本質(zhì)區(qū)別野狼网址、奇異性與系統(tǒng)模型和系統(tǒng)負載的聯(lián)系538免费精品视频、結(jié)構(gòu)保持能量函數(shù)法可能具有的內(nèi)在保守性等，這對深入理解電力系統(tǒng)微分代數(shù)方程模型的拓撲結(jié)構(gòu)大学情侣酒店、結(jié)構(gòu)保持能量函數(shù)法和暫態(tài)電壓穩(wěn)定及其與功角穩(wěn)定的關(guān)系具有一定的價值99精品这里只有精品。

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先www.色视频在线，文中列舉了Ken Shoemake提出的點點生成的球面Bezier曲線(第一類球面Bezier曲線)的性質(zhì)，如端點性質(zhì)五月丁香六月综合欧美在线观看、對稱性質(zhì)手机在线看片91、運動不變性質(zhì)、球面凸包性質(zhì)等桃色阁国产精品，并指出這種球面Bezier曲線沒有剖分性質(zhì)国产美女爆乳主播在线播放；基于細分，文中給出了一種新的球面Bezier曲線(第二類球面Bezier曲線)的構(gòu)造方法综合久久本道中文字幕www，指出這種曲線是連續(xù)可微的96人人操人人干人人；作為這些理論的應(yīng)用，文中改進了Ken Shoemake提出的球面插值曲線構(gòu)造方法中文字幕日韩专区最新；進一步国产在线无码全黄，文中探討了Bezier曲線在更廣泛的流形上的推廣方法。2球面Chaikin算法和一般的球面割角算法国产性色AV网址无毒不卡。