Journal of Lie Theory 34 (2024), No. 4, 773--783
Copyright Heldermann Verlag 2024
Lie Groups Endowed with a Left Invariant Riemannian Metric and a Flat Metric Connection with Skew-Symmetric Torsion
Mohamed Boucetta
Faculté des Sciences Gueliz, Université Cadi-Ayyad, Marrakech, Morocco
m.boucetta@uca.ac.ma
Hicham Lebzioui
École Supérieure de Technologie-Khénifra, Sultan Moulay Slimane University, Khénifra, Morocco
hlebzioui@gmail.com
We give a complete description of Lie groups endowed with a left invariant Riemannian metric and a left invariant flat metric connection with skew-symmetric torsion.
Keywords: Lie groups, Lie algebras, flat metric connections, matched pair of Lie algebras.
MSC: 53B05, 53C20; 22E15, 22E60.
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