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A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach |
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| Authors: | Oldřich Kowalski Barbara Opozda Zdeněk Vlášek |
| Institution: | (1) Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic;(2) Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland |
| Abstract: | The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver 7]. |
| Keywords: | Two-dimensional manifolds with affine connection locally homogeneous connections Lie algebras of vector fields Killing vector fields |
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