黎曼度量 的英文怎麼說

中文拼音 [límàndùliáng]
黎曼度量 英文
metric tensor
  • 黎 : Ⅰ名詞1 （黎族） the li nationality one of the national minorties in hainan province2 [書面語] （...
  • 曼 : 曼形容詞1. （柔和） graceful; soft and beautiful 2. （長） prolonged; long-drawn-out
  • 度 : 度動詞[書面語] （推測; 估計） surmise; estimate
  • 量 : 量動1. （度量） measure 2. （估量） estimate; size up
  • 黎曼 : bernhard riemann
  • 度量 : 1. （計量長短） measure; metric; mensuration 2. （寬容人的限度） tolerance; magnanimity
  1. ( 2 ) the liman problem is normally adopted to check the liability of numerical method. the calculation error was within 9 % by comparison with the theoretic solutions of liman problem in the following case, the dimensionless calculation length was 2 with high pressure zone 0. 8, and the dimensionless state parameters were p1 = 2, p2 = 1, p1 = p2 = 1, u1 = u2 = 0. experiment results in literature [ 8 ] were used to check the adaptability of the numerical model developed here for unconfined gas cloud explosions and the calculation error was within 13 %

    （ 2 ）數值方法的可靠性通常用黎曼問題的解析解檢驗，本文以無量綱計算區長度為2 ，高壓區長度為0 . 8 ，狀態參數為p _ 1 = 2 ， p _ 2 = 1 ， _ 1 = _ 2 = 1 ， u _ 1 = u _ 2 = 0條件下的黎曼問題解析解對所編制的爆炸場計算程序進行了考核，結果表明該程序的計算誤差在9以內；為考核本文計算模型預測開敞空間氣雲爆炸的適用性，以文獻[ 8 ]的實驗數據進行了校核，計算誤差在13以內。
  2. 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 ] 。
  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。
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