metric geometry 中文意思是什麼

metric geometry 解釋
度量幾何學
  • metric : adj. 1. 公制的，米制的；十進制的；習慣于用公制的。2. 度量的。
  • geometry : n. 1. 幾何學。2. 幾何形狀。3. 幾何學著作。
  1. Lots of concrete examples are (, ) - metrics. and one of fundamental problems in finsler geometry is to find and study finsler metrics with constant ( flag ) curvature. on the basic, we majarly study the following problems in present paper : ( a ) to the property of a class of (, ) - metrics in which is parallel with respect to riemann metric a and riemann metric a is of constant curvature, we obtain the following theorem4. 3 let f (, ) be a positive definite metric on the manifold m ( dimm > 3 )

    在finsler幾何中，我們現在已知的finsler度量已經很多了，但大多數具體的例子主要都集中在（ ， ） ?度量中，又在finsler幾何中一個基本的問題就是去發現和研究具有常曲率的finsler度量，基於這些本文主要研究了以下一些問題： （ a ）一類關於是平行的並且riemann度量具有常曲率的（ ， ） ?度量的特殊性質，得到了如下的定理4
  2. On the other hand, the conformal deformation ' s 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. the problem that the conformal gauss curvature equation may have a solution for every nonegative holder continuous function k ( x ) is also an open problem

    ） = 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幾何分析中的一個重要問題。當預定的函數k取正值時，共形高斯曲率方程解的存在性命題作為一個猜測至今未得到解決。
  3. Harmonic maps between riemannian manifolds are very important in both differential geometry and mathematical physics. riemannian manifold and finsler manifold are metric measure space, so we can study harmonic map between finsler manifolds by the theory of harmonic map on general metric measure space, it will be hard to study harmonic map between finsler manifolds by tensor analysis and it will be no distinctions between the theory of harmonic map on finsler manifold and that of metric measure space. harmonic map between riemannian manifold also can be viewed as the harmonic map between tangent bundles of source manifold and target manifold

    黎曼流形間的調和映射是微分幾何和數學物理的重要內容。黎曼流形和finsler流形都是度量空間，自然可利用一般度量空間調和映射的理論討論finsler流形間的調和映射。但由於控制finsler流形性質的各種張量一般情況下很難應用到一般度量空間調和映射的理論中，使得這樣的討論大都是形式上的，並與一般度量空間調和映射的理論區別不大。
  4. Its propositions hold as well for objects made of rubber as for the rigid figures encountered in metric geometry

    拓撲學的一些定理適用於橡膠製成的（可變形的）物體，也同樣適用於在度量幾何學中討論的剛性圖形。
  5. Some intrinsic metrics in differential manifolds, such as cara - theodory metrics and kobayashi metrics in complex manifolds, are finsler metrics. finsler metrics is just riemannian metrics without quadratic restriction, which was firstly introduced by b. riemann in 1854. the geometry with finsler metric is called finsler geometry

    Finsler度量是沒有二次型限制的riemann度量， riemann在1854年的就職演說中已經涉及了這種情形。以finsler度量為基礎的幾何學被稱為finsler幾何。
  6. This paper mainly study the relations between some algebraic properties of roe algebras and the coarse geometry of metric spaces, and its applications to the reduced crossed product c - algebras and the coarse baum - connes conjecture. the paper consists of two chapters

    本文主要研究這類c ~ * -代數的某些性質與底空間幾何之間的聯系及其在交叉積c ~ * -代數和粗baum - connes猜測中的應用。
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