Geodesic
On Metrizable Locally Homogeneous Connections in Dimension
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 157-166.

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We discuss metrizability of locally homogeneous affine connections on affine 2-manifolds and give some partial answers, using the results from [Arias-Marco, T., Kowalski, O.: Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds. Monatsh. Math. 153 (2008), 1–18.], [Kowalski, O., Opozda, B., Vlášek, Z.: A classification of locally homogeneous connections on 2-dimensional manifolds vis group-theoretical approach. CEJM 2, 1 (2004), 87–102.], [Vanžurová, A.: On metrizability of locally homogeneous affine connections on 2-dimensional manifolds. Arch. Math. (Brno) 49 (2013), 199–209.], [Vanžurová, A., Žáčková, P.: Metrizability of connections on two-manifolds. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 48 (2009), 157–170.].
Classification : 53B05, 53B20
Keywords: Manifold; affine connection; Riemannian connection; Lorentzian connection; Killing vector field; locally homogeneous space 
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Vanžurová, Alena. On Metrizable Locally Homogeneous Connections in Dimension. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 157-166. http://geodesic.mathdoc.fr/item/AUPO_2016__55_1_a16/