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].
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Kowalski, O., Opozda, B. & Vlášek, Z. A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach. centr.eur.j.math. 2, 87–102 (2004). https://doi.org/10.2478/BF02475953
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DOI: https://doi.org/10.2478/BF02475953
Keywords
- Two-dimensional manifolds with affine connection
- locally homogeneous connections
- Lie algebras of vector fields
- Killing vector fields