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- It had been proved that the curvature tensor is a curl(grad),not zero except in Eucldean space,and so discovered the essence of Bianchi identity:div(rot(grad))=0,the curvature,forming tube field,is invariant along the tube,i. 證實 :曲率它正是非歐氏空間不為零的梯度的旋度 .;並發現 :Bianchi等式實質是div(rot(grad) ) =0;曲率形成管形場;沿管不變
- The more general case of a tensor field is similar but more complicated. 較普遍的張量場情況大致相似，但是更為複雜。
- At the same time,The curvature tensor expression of a Riemannian manifold under the special semi-symmetric metric-recurrent connections is also obtained. 同時給出了特殊半對稱聯絡的黎曼流形曲率張量表示。
- In Riemannian manifolds, one studies Riemannian metric, covariant derivative, Riemannian connection, basic properties of the Riemann curvature tensor, curvature forms etc. 黎曼流形部分主要涉及黎曼度量，黎曼流形的定義，切向量場的協變微分，黎曼聯絡，黎曼幾何的基本定理，曲率張量，曲率形式等概念和理論。
- In this paper, we investigate the whole formulas of the curvature tensor, Ricci curvature and scalar curvature on the singly and doubly warped product on Lorentzian manifolds. 給出了洛倫茨流形上的曲率張量、純量曲率的計算公式;並推導出了洛倫茨流形上的二重扭積公式.
- curvature tensor of an affine connection 仿射聯絡的曲率張量
- Curvature Tensor of Riemannian Manifold 關於黎曼流形的曲率張量
- harmonic Mobius curvature tensor 調和Mobius曲率張量
- Secondly, the diffusion tensor field of the gray image at each pixel is calculated and applied to construct weighted gradient field, thus to create a divergence-based colorization equation. 然後計算每個像素的擴散張量，並利用這些擴散張量構造加權梯度場，從而導出基於散度的圖像彩色化方程；
- harmonic Riemannian curvature tensor 調和Riemann曲率張量
- A nonlinear tensor-valued weighted directional-distance filtering method is proposed for regularizing the diffusion tensor field produced by diffusion tensor magnetic resonance imaging. 為了正則化擴散張量磁共振成像所產生的擴散張量場，提出了一種非線性張量值加權方向-距離濾波方法。
- tensor field of complex structure 張量場
- alternating covariant tensor field 共變交錯張量場
- Curvature tensors, gauge field are actually curl field of gradient 曲率張量,規範場的實質:梯度的旋度場
- Suanifolds with the Vanishing Normal Curvature Tensor in Locally Syetric Space 局部對稱黎曼流形中法曲率張量場消失的子流形
- THE RICCI AND BOCHNER TYPE CURVATURE TENSOR OF CONTACT RIEMANNIAN STRUCTURE Contact黎曼結構的Ricci與Bochner型曲率張量
- Yes, if we write them as rank-2 symmetric tensor fields, they satisfied Einstein equation.However, it is not clear how big a deal this is, since diffeomorphism is put in before hand. 在近似下，弦論可以得出廣義相對論，從而一切證實廣義相對論的實驗都是對弦論的支持。
- The field artillery pounded away at the for tress. 野戰炮兵連續炮擊那座要塞。
- The Invariant of Projective Transformation of Semisymmetric Metric-recurrent Connections and Curvature Tensor Expressions 半對稱度量循環聯絡射影變換的不變數及曲率張量表示
- The crowd cheered as the teams entered the field. 球隊入場時觀眾們為之歡呼。
