论文标题
统一组的SVD关闭亚组：广义主对数和最小化的测量学
SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics
论文作者
论文摘要
我们研究了属于连接的SVD封闭的子组$ g $ $ u_n $的任何矩阵的对数的广义主体$ \ mathfrak {g} $ - lie algebra $ \ mathfrak {g} $。该集合是有限数量的子集与同质空间的非相互不相交联合，它与合适的一组最小化的大地测量学有关。该组$ g $的许多特殊案例已明确分析。
We study the set of generalized principal $\mathfrak{g}$-logarithms of any matrix belonging to a connected SVD-closed subgroup $G$ of $U_n$, with Lie algebra $\mathfrak{g}$. This set is a non-empty disjoint union of a finite number of subsets diffeomorphic to homogeneous spaces, and it is related to a suitable set of minimizing geodesics. Many particular cases for the group $G$ are explicitly analysed.
