切丛

本文给出了矢丛上Sasaki度量的局部表示，特别得到单位切丛T1S~（2n+1）上Sasaki度量的表达式。

In this paper , we give an explicit representation of the Sasaki metric on a vector bundle . In particular , we get Sasaki metric on unit tangent bundle T_1S ~ ( 2n + 1 ), by which we calculate the volume of the Hopf vector field V_h .

从向量函数微分去看切丛上的联络

Observe connection of tangent bundle through the Differentiable of vector function

采用切丛TS2n+1上的不同联络，证明了Hopf向量场是S2n+1上体积最小的单位向量场。

With a Sasaki metric defined by Hopf vector field , we show that the Hopf vector field has minimum volume on S2n + 1 for all n.

第四节分别选择切丛和主丛作为系统的状态空间，根据它们的特点，建立了切丛和主丛上的微分动力系统并推导出了它们的局部坐标表示。

In section 4 , the representations which are about local coordinate of the differential dynamic systems on principal bundle and tangent bundle are discussed .

本文利用可定向3-流形切丛的平凡性，在3维几何上建立了一种整体标架法。

In this paper , the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology .

利用李代数胚的对偶丛上有自然诱导的泊松结构，.构造出了同一余切丛上的不同的辛群胚结构，推广了辛群胚的性质。

By using the nature induced Poisson structure on the dual bundle of lie algebroids , we construct two different symplectic groupoids structures on the same cotangent bundle , and extend properties of the symplectic groupoids .

关于黎曼空间的切纤维丛主丛与刚体运动

ON THE BUNDLES OF ORIENTED m-PLANES OF A RIEMANN SPACE . Principal Fibre Bundle and Motion of Rigid Body