finsler geometry 中文意思是什麼
-
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 -
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。 -
The non - riemannian geometric quantities in finsler geometry describe the difference between finsler geometry and riemann geometry
Finsler幾何中的非黎曼幾何量刻畫的是finsler幾何與黎曼幾何的不同之處。 -
The study of these quantities is benefit for us to make out their distinction and the nature of finsler geometry
對這些量進行研究有利於我們看清楚它們之間的差異，並且對認清finsler幾何的廬山真面目有十分重要的作用。 -
Now there are two methods on the resarch of finsler geometry. one shi tensor method, the other is analytic method. in present papaer, we majorly use the lat tor
對于finsler幾何的研究，現在主要有兩種方法，一種是張量的方法，一種是分析的方法，本文主要採用了後者。 -
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。
分享友人