论文标题
地球方程与Riemannian歧管上的GCH之间的类比
Analogy between geodesic equation and the GCHS on Riemannian manifolds
论文作者
论文摘要
由GCHS \脚注{GCHS：广义的协变汉密尔顿系统\\ GSPB之间的相似方程式形式开启：Geospin变量表达的Geodesic方程所定义的广义结构性泊松托架}，我们找到了Geospin Matrix和S-Dynamist之间的深厚连接。以这种对比方式，我们实际上证明了GCHS是一种适合原始所述的弯曲时空的兼容理论。相比之下，Riemannian几何形状中的Geospin矩阵具有与GCHS中的S-Dynemics相同的物理性质。我们获得了一个事实，即，GCH可以自然地从速度场上衍生。 我们严格证明了几何$ \ hat {s} {{{\ left（{{x} _ {k}}}，{{p} _ {i}}，h \ right）}^{ {{B} _ {k}}，{{a} _ {i}}，w \ right）}^{t}} $通过使用结构运算符$ \ hat {s} $直接由结构衍生的$ {a} $ {a} $ {i} $ ______________ $ {p} _ {i} $和汉密尔顿$ h $。显然，它证明了Riemannian歧管上的GCHS肯定是由Christoffel符号决定的。作为应用程序，我们考虑了Riemannian几何形状上的GCH。
Enlightened by the similar equation form between the GCHS \footnote{GCHS: Generalized Covariant Hamilton System\\GSPB:Generalized structural Poisson bracket} defined by the GSPB and the geodesic equation expressed by geospin variable, we find a deep connection between the geospin matrix and S-dynamics. In this contrastive way, we actually proves that the GCHS is a compatible theory suitable for the curved spacetime as primitively stated. By contrast, geospin matrix in Riemannian geometry has the same physical nature as S-dynamics in GCHS. We obtain a fact that geodesic equation can be naturally derived by the GCHS in terms of the velocity field. We strictly prove that the geometrio $\hat{S}{{\left( {{x}_{k}},{{p}_{i}},H \right)}^{T}}={{\left( {{b}_{k}},{{A}_{i}},w \right)}^{T}}$ holds by using structural operator $\hat{S}$ directly induced by structural derivative ${A}_{i}$ in terms of position ${x}_{k}$, momentum ${p}_{i}$ and Hamiltonian $H$ respectively. It evidently proves that the GCHS on the Riemannian manifold is certainly determined by the Christoffel symbols. As an application, we consider the GCHS on Riemannian geometry.
