Geodesic
On Metrizable Locally Homogeneous Connections in Dimension
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 157-166 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.].
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/

[1] Arias-Marco, T., Kowalski, O.: Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds. Monatsh. Math. 153 (2008), 1–18. | DOI | MR | Zbl

[2] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry I, II. Wiley-Intersc. Publ., New York, Chichester, Brisbane, Toronto, Singapore, 1991.

[3] Kowalski, O., Opozda, B., Vlášek, Z.: Curvature homogeneity of affine connections on two-dimensional manifolds. Coll. Math. 81, 1 (1999), 123–139. | DOI | MR | Zbl

[4] Kowalski, O., Opozda, B., Vlášek, Z.: A Classification of Locally Homogeneous Affine Connections with Skew-Symmetric Ricci Tensor on 2-Dimensional Manifolds. Monatsh. Math. 130 (2000), 109–125. | DOI | MR | Zbl

[5] 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. | MR

[6] Mikeš, J., Stepanova, E., Vanžurová, A.: Differential Geometry of Special Mappings. Palacký University, Olomouc, 2015. | MR | Zbl

[7] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. Palacký University, Olomouc, 2009. | MR | Zbl

[8] Olver, P. J.: Equivalence, Invariants and Symmetry. Cambridge Univ. Press, Cambridge, 1995. | MR | Zbl

[9] Opozda, B.: A classification of locally homogeneous connections on 2-dimensional manifolds. Diff. Geom. Appl. 21 (2004), 173–198. | DOI | MR | Zbl

[10] Singer, I. M.: Infinitesimally homogeneous spaces. Comm. Pure Appl. Math. 13 (1960), 685–697. | DOI | MR | Zbl

[11] Vanžurová, A., Žáčková, P.: Metrization of linear connections. Aplimat, J. of Applied Math. (Bratislava) 2, 1 (2009), 151–163.

[12] Vanžurová, A., Žáčková, P.: Metrizability of connections on two-manifolds. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 48 (2009), 157–170. | MR | Zbl

[13] Vanžurová, A.: On metrizability of locally homogeneous affine connections on 2-dimensional manifolds. Arch. Math. (Brno) 49 (2013), 199–209. | MR

[14] Vanžurová, A.: On metrizability of a class of 2-manifolds with linear connection. Miskolc Math. Notes 14, 3 (2013), 311–317. | MR | Zbl