finsler manifold 中文意思是什麼
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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 -
The second part consist of chapter four. in chapter one, we study the energy density of harmonic map from finsler manifold and generalize classical result in [ se ]. in chapter two, we obtain lower estimates for the first eigenvalue of the laplace operator on a compact finsler manifold, and it generalize lichnerowicz - obata theorem [ li ] [ ob ]. in chapter three, we derive the first and second variation formula for harmonic maps between finsler manifolds. as an application, some nonexistence theorems of nonconstant stable harmonic maps from a finsler manifold to a riemannian manifold are given
第一章討論finsler流形到黎曼流形調和映射的能量密度的間隙性，推廣了[ se ]中的結果。第二章對緊致finsler流形上laplace運算元的第一特徵值的下界作了估計，推廣了黎曼流形上的lichnerowicz - obata定理[ li ] [ ob ] 。 -
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。 -
When target manifold is r, . if u is a function of finsler manifold, we can define laplace operator, it is well - defined. if u is called the eigenvalue of the laplacian a and u is called the corresponding eigenfunction
眾所周知，對于黎曼幾何，調和映射是調和函數的推廣，且當目標流形為r時，二（喲二撇el ] .因此對于屍『 nsler流形m上的函數。可以定義laptace運算元為。 -
One of open problems is to study harmonic maps between finsler manifolds and derive the first and second variation formula for harmonic maps between finsler manifolds. firstly, we define harmonic map between finsler manifold. in fact, it is the harmonic map from projective sphere bundle of source manifold to the projective sphere bundle of target manifold
運算元的第一非零特徵值凡全mk .特別地，當『 ，二二k時， m的直徑為六?當m是黎曼流形時，由moer 「定理的推論直接可知m與半徑為去的球等距 -
Let ( m, f ) be an n - dimensional compact finsler manifold without boudary. if for some positive constant k, then moreover, the diameter of m is when 1 = mk
設m是緊致無邊的m維幾二le :流形，如果存在常數k ，使得b凡引x ）全（ 。
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