Geodesic
Normal connections on three-dimensional homogeneous spaces with a non-solvable transformation group. I. A non-solvable stabilizer
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 61-76

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In this paper we present a complete local classification of three-dimensional homogeneous spaces admitting a normal connection. We consider only the case of a non-solvable Lie group of transformations with a non-solvable stabilizer. The local classification of homogeneous spaces is equivalent to the description of effective pairs of Lie algebras. We describe all invariant affine connections on those homogeneous spaces together with their curvature and torsion tensors. We study the holonomy algebras of homogeneous spaces and find when the invariant connection is normal. We use an algebraic approach for describing the connections as well as methods of the theories of Lie groups, Lie algebras and homogeneous spaces.
Keywords: normal connection, homogeneous space, holonomy algebra.
Mots-clés : transformation group 
@article{UZKU_2013_155_4_a6,
     author = {N. P. Mozhei},
     title = {Normal connections on three-dimensional homogeneous spaces with a~non-solvable transformation {group.~I.} {A~non-solvable} stabilizer},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {61--76},
     publisher = {mathdoc},
     volume = {155},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a6/}
}
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N. P. Mozhei. Normal connections on three-dimensional homogeneous spaces with a non-solvable transformation group. I. A non-solvable stabilizer. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 61-76. http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a6/