Geodesic
Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion
Journal of Lie theory, Tome 34 (2024) no. 2, pp. 339-352
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For a general affine connection with parallel torsion and curvature, we show that a post-Lie algebra structure exists on its space of vector fields, generalizing previous results for flat connections. However, for non-flat connections, the vector fields alone are not enough, as the presence of curvature also necessitates that we include endomorphisms corresponding to infinitesimal actions of the holonomy group. We give details on the universal Lie algebra of this post-Lie algebra and give applications for solving differential equations on manifolds.
Classification : 53C05, 41A58, 53C30,17D99
Mots-clés : Post-Lie algebras, connections, locally homogeneous spaces spaces 
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     title = {Post-Lie {Algebra} {Structure} of {Manifolds} with {Constant} {Curvature} and {Torsion}},
     journal = {Journal of Lie theory},
     pages = {339--352},
     year = {2024},
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E. Grong; H. Z. Munthe-Kaas; J. Stava. Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion. Journal of Lie theory, Tome 34 (2024) no. 2, pp. 339-352. http://geodesic.mathdoc.fr/item/JLT_2024_34_2_JLT_2024_34_2_a3/