In this thesis,we mainly study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. We study the topology of these manifolds via comparisonal geometry methods.In chapter 1 ,we will make a general description on the recent researches in our field.

在本文中18禁止看污污网站在线看，我們主要研究了Ricci曲率有下界完備非緊的Riemann流形的拓?fù)鋯?wèn)題国产美女一级特黄A级APP全部，在比較幾何的基礎(chǔ)上研究了有特定曲率條件的Riemann流形的拓?fù)洌玫搅擞嘘P(guān)其拓?fù)浣Y(jié)構(gòu)的一些結(jié)果亚洲无码第32页。

In Chapter 5, the least-squares solutions bisymmetric matrix set of the matrix equation ATXA = B on two linear manifolds Si ={X BSRnxn\\\XY - Z\\ = min} and S2 ={X BSRnXn\XY = Z, YtTZi = ZjYu ZtffYi = Zi,i = 1,2, Y, Z e Rnxm}, by applying the singular value decomposition of matrix and the canonical correlation decomposition of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = B on two linear manifolds.

在第五章亚洲日韩激情无码一区，我們研究了兩類(lèi)線性流形S_1={X∈BSR~|‖XY-Z‖=min}和S_2={X∈BSR~|XY=Z，Y_i~TZ_i=Z_i~TY_i日韩不卡中文字幕在线看，Z_iY_i+Y_i=Z_i国产高清一级A片在线视频爱微，i=1国产Aⅴ一区二区三区四区，2，Y黄色国产免费国产，Z∈R~}上矩陣方程A~TXA=B的雙對(duì)稱最小二乘解黄黄色色爱爱网。

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章給出了以環(huán)面作為邊界的兩個(gè)3維流形在作融合積時(shí)不產(chǎn)生新的不可壓縮曲面的一個(gè)充分必要條件国产在线一区二区三区麻豆，并將這個(gè)結(jié)果與關(guān)于環(huán)面到自身的自同胚類(lèi)的分類(lèi)的結(jié)果相結(jié)合久久久久精品日韩久久久，證明了本文的一個(gè)核心結(jié)論，即存在無(wú)窮多個(gè)互不同胚的3維流形滿足除了一個(gè)環(huán)面以外不含有其他的不可壓縮曲面欧美一级夜夜爽。

The first 10 chapters study cohomolgy of open set in Euclidean space,treat smooth manifolds and their cohomology and end with integration on manifolds.

全書(shū)分四章：范疇與函子及其在模論中的應(yīng)用黄色视频免在线观看免费；特殊模與相應(yīng)的維數(shù)；環(huán)模復(fù)形的同調(diào)理論九九在线精品免费视频；譜序列黄色视频在线观看视频在线播放。

Ballast manifolds shall be equipped with not immersed shut off valves separating the system in three sections each one separately connectable to the suction and delivery manifolds of each one of the two pumps and to the sea chests.

壓載總管應(yīng)配有不會(huì)被浸到的截止閥，截止閥將系統(tǒng)分割為獨(dú)立的三段（左舷段自拍高潮日韩在线视频播放免费观看、中部段和右舷段）精品国产福利第一区二区，每個(gè)截止閥都可獨(dú)立地與吸口相連并可將兩臺(tái)泵中的任何一臺(tái)的總管輸送到海底門(mén)。

Using the continuity method, we will obtain a theorem of existence of solutions to the equation on 4-dimensional compact Riemannian Manifolds.Finally, we will consider a kind of Kazdan-Warner type equation on compact complex manifolds.

作為上述工作的補(bǔ)充国产一区精品福利，我們討論了規(guī)范固定Yang-Mills方程免费看毛视频，并用連續(xù)性方法得到了一個(gè)在四維緊致黎曼流形上解的存在性定理。

Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann給出的久久综合加勒比金8天国，早期的有關(guān)類(lèi)流形的研究與物理和力學(xué)密切相關(guān)色色色色综合网站，自從1991年金行壯二發(fā)表了陪集空間上存在不變仿凱勒結(jié)構(gòu)的代數(shù)化結(jié)果后，李群及李代數(shù)理論在這類(lèi)流形的研究中起著主要作用亚洲黄色，特別地亚洲经典一区二区三区，李代數(shù)的雙極化與這類(lèi)流形密切相關(guān)，半單李代數(shù)的雙極化的相關(guān)幾何a人人操人人干，金行壯二欧美就要操，候自新和鄧少?gòu)?qiáng)等人已作了研究，二次李代數(shù)是比半單李代數(shù)更廣且?guī)в蟹峭嘶蛔冸p線性型的李代數(shù)麻花豆传媒剧国产剧免费，本文主要研究了二次代數(shù)的雙極化及相關(guān)幾何男男无码免费专区男人的天堂。

In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.

在這篇文章中我們定義了射影Blaschke流形的概念，將等仿射微分幾何的理論推廣到了射影Blaschke流形亚洲簧片AB在线观看，并證明：如果n維完備射影Blaschke 超球面 M 的通用覆蓋流形分別是完備的拋物型欧美性交三级视频、橢圓型或雙曲型仿射球，則M分別是n維歐氏空間一二三区无卡高清视频在线播放、n維超球面或n維單位圓盤(pán)關(guān)于各自空間的一個(gè)等距離散子群的商亚洲毛片不卡88AV在线，從而對(duì)完備射影Blaschke 超球面進(jìn)行了分類(lèi)。

In differentiable manifolds, one studies for instance differentiable structure, definition of differential manifolds, diffeomorphism, tangent space, Embedding theorem, partitions of unity etc.

微分流形部分主要涉及微分結(jié)構(gòu)，微分流形的定義及例子性交毛片视频免费看，可微映射欧洲精品乱码久久久久，微分同胚，切空間與余切空間日韩孕妇自拍视频直播在线观看网站，流形的嵌入毛片点击进入免费看，單位分解定理等。

In Chapter 2,we give some preparations about the basic knowledge of 4-manifolds, spin 4-manifolds and group actions on manifolds....

主要介紹了4-流形的基本概念少妇AA毛片在线播放，4-流形上的Spin幾何以及流形上的群作用等方面的基本知識(shí)欧美日韩在线观看。