SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics

Autor:	Pertici, Donato, Dolcetti, Alberto
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry 53C30 15B30 22E15
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.11716 Zobrazit plný text záznamu View this record from Arxiv