On Locally Symmetric 3-Dimensional Riemannian Lie Groups

2016/07/07 by Romain, Nimpa Pefoukeu, Jean, Wouafo Kamga, Bertrand, Djiadeu Ngaha Michel
#53C20 #53C30 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.01950

Abstract

In this paper, we use the powerful tool Milnor bases to classify all the 3-dimensional connected and locally symmetric Riemannian Lie Groups by solving system of polynomial equations of structure constants of each Lie algebra . Moreover, we showed that E₀(2), is the only Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric.

Related

• Homogeneous structures of 3-dimensional Lie groups
• The index of symmetry for a left-invariant metric on a solvable\n three-dimensional Lie group
• Milnor-type theorems for left-invariant Riemannian metrics on Lie groups
• The index of symmetry of three-dimensional Lie groups with a\n left-invariant metric
• On Z-decomposition of some euclidian lie algebras