论文标题
谎言组值函数的高阶喷气捆
Higher order jet bundles of Lie group-valued functions
论文作者
论文摘要
对于每个正整数$ k $，$ k $ jet的功能的束从平滑的歧管，$ x $到谎言组，$ g $，用$ j^k（x，g）$表示，并且在规范上赋予了$ x $的谎言组结构。在这项工作中，我们利用线性连接来琐碎这个捆绑包，即，将其从$ j^k（x，g）$构建到超过$ g $的矢量捆绑包中。之后，我们给出了在琐碎空间上的群体乘法的显式表达，以及逆元素的公式。在最后一节中，考虑了$ x $的协调图，并计算了琐碎化的局部表达。
For each positive integer $k$, the bundle of $k$-jets of functions from a smooth manifold, $X$, to a Lie group, $G$, is denoted by $J^k(X,G)$ and it is canonically endowed with a Lie groupoid structure over $X$. In this work, we utilize a linear connection to trivialize this bundle, i.e., to build an injective bundle morphism from $J^k(X,G)$ into a vector bundle over $G$. Afterwards, we give the explicit expression of the groupoid multiplication on the trivialized space, as well as the formula for the inverse element. In the last section, a coordinated chart on $X$ is considered and the local expression of the trivialization is computed.
