论文标题
对连接的谎言组的谎言指数衍生物规范的估计
Estimates for the norm of the derivative of Lie exponetial map for connected Lie groups
论文作者
论文摘要
让$ g $是一个真正的连接的谎言组，其左不变度度量$ d $，$ \ mathfrak {g} $它的lie代数。在本文中，我们为$ | d \ exp_ {x}（y）|，\ x，y \ in \ mathfrak {g} $提供了一组有趣的上限和下限。如果$ \ textrm {ad} _x $是对角线的，则这些范围仅取决于$ \ textrm {ad} _x $的特征值，但通常它们是奇异值$ \ textrm {ad ad} _x _x _x $的函数。
Let $G$ be a real connected Lie group with a left invariant metric $d$, $\mathfrak{g}$ its Lie algebra. In this paper we present a set of interesting upper and lower bounds for $|d\exp_{x}(y)|,\ x,y \in \mathfrak{g}$. If $\textrm{ad}_x$ is diagonalizable, these bounds only depend on eigenvalues of $\textrm{ad}_x$, but in general they are functions of the singular values $\textrm{ad}_x$.
