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

arXiv2212.11716MaRDI QIDQ6421376

Donato Pertici, Alberto Dolcetti

Publication date: 22 December 2022

Abstract: We study the set of generalized principal $mathfrakg$-logarithms of any matrix belonging to a connected SVD-closed subgroup $G$ of $U_n$, with Lie algebra $mathfrakg$. 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.

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General properties and structure of real Lie groups (22E15) Matrix Lie algebras (15B30)

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