论文标题
基于地球方程的几何动力学，带有Riemannian歧管上的cartan结构方程
Geometrodynamics based on geodesic equation with Cartan structural equation on Riemannian manifolds
论文作者
论文摘要
由Geospin Matrix $ W $作为Riemannian几何形状的新变量激励。然后，我们使用四个真实的动力学变量$ \ left \ {a，α，v，w \ right \} $来显示cartan结构方程的动态本质，我们在\ begin \ begin {align}}以下表示的riemannian歧管上获得了几何差异。 ＆θ/d {{t}^{2}} = a-v \ wedge w，\ nonumber ＆dθ/d {{t}^{3}} = v \wedgeα-a \ wedge w，\ nonumber ＆ω/d {{t}^{2}} =α-w \ wedge w，\ nonumber ＆dΩ/d {{t}^{3}} = w \ w \ w \ w \ w \ w \ wedge w \ nonumber \ end \ end {align}，该{align}对于主捆绑包中的任何连接都更有效。我们可以看到，第一个方程式很好地解释了地球方程，第二个公式表示第一个Bianchi身份，而最后一个方程式揭示了第二个Bianchi身份的动力学性质。这意味着可以根据Geospin矩阵以实际的几何动力学形式来重写Riemannian歧管上的Cartan结构方程。
Motivated by the geospin matrix $W$ as a new variable in Riemannian geometry. Then, we use four real dynamical variables $\left\{ a,α,v,W \right\}$ to show the dynamical essence of Cartan structural equation, we obtain the geometrodynamics on Riemannian manifolds that can be expressed below \begin{align} & Θ/d{{t}^{2}}=a-v\wedge W,\nonumber & dΘ/d{{t}^{3}}=v\wedge α-a\wedge W,\nonumber & Ω/d{{t}^{2}}=α-W\wedge W, \nonumber & dΩ/d{{t}^{3}}=W\wedge α-α\wedge W\nonumber \end{align} that is valid more generally for any connection in a principal bundle. We can see that the first equation explains the geodesic equation very well, the second formula means the first Bianchi identity, while the last equation reveals the dynamical nature of the second Bianchi identity. It implies that Cartan structural equations on Riemannian manifolds can be rewritten in a real geometrodynamical form based on the geospin matrix.
