This article is cited in 2 scientific papers (total in 2 papers)
On isometries of some Riemannian Lie groups
V. V. Gorbatsevich
We study isometry groups of Lie groups endowed with left-invariant Riemannian metrics. We mainly consider triangular Lie groups. By the familiar Gordon–Wilson theorem, calculating the isometry groups of left-invariant metrics on such groups is reduced to calculating the automorphism groups of the corresponding Lie algebras and to distinguishing compact
subgroups of these groups. We consider nilpotent Lie groups in more detail, with special attention to filiform Lie groups and their relatives (prefiliform, quasifiliform). As a rule, we state the main results in terms of the automorphism groups of Lie algebras and then give their
geometric interpretation. Special attention is paid to finding the group of connected components of the isometry group (in particular, it is calculated for all filiform Lie groups) and to conditions
guaranteeing that the group of rotations (that is, isometries preserving a given point) is finite for certain classes of Riemannian Lie groups.
PDF file (2182 kB)
Izvestiya: Mathematics, 2002, 66:4, 683–699
MSC: 53C30, 17B40, 22E25
V. V. Gorbatsevich, “On isometries of some Riemannian Lie groups”, Izv. RAN. Ser. Mat., 66:4 (2002), 27–46; Izv. Math., 66:4 (2002), 683–699
Citation in format AMSBIB
\paper On isometries of some Riemannian Lie groups
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Zhiguang Hu, Shaoqiang Deng, “Three dimensional homogeneous Finsler manifolds”, Math. Nachr, 2012, n/a
Payne T.L., “Applications of Index Sets and Nikolayevsky Derivations To Positive Rank Nilpotent Lie Algebras”, J. Lie Theory, 24:1 (2014), 1–27
|Number of views:|