Lie Groups Endowed with a Left Invariant Riemannian Metric and a Flat Metric Connection with Skew-Symmetric Torsion

M. Boucetta; H. Lebzioui

doi:10.5802/jolt.1360

M. Boucetta; H. Lebzioui

Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 773-783

Abstract

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.

Zbl

DOI: 10.5802/jolt.1360

Classification: 53B05, 53C20, 22E15, 22E60
Keywords: Lie groups, Lie algebras, flat metric connections, matched pair of Lie algebras

@article{JOLT_2024_34_4_a1,
     author = {M. Boucetta and H. Lebzioui},
     title = {Lie {Groups} {Endowed} with a {Left} {Invariant} {Riemannian} {Metric} and a {Flat} {Metric} {Connection} with {Skew-Symmetric} {Torsion}},
     journal = {Journal of Lie Theory},
     pages = {773--783},
     year = {2024},
     volume = {34},
     number = {4},
     doi = {10.5802/jolt.1360},
     zbl = {1559.53020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1360/}
}

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M. Boucetta; H. Lebzioui. Lie Groups Endowed with a Left Invariant Riemannian Metric and a Flat Metric Connection with Skew-Symmetric Torsion. Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 773-783. doi: 10.5802/jolt.1360

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