×

On metrizable locally homogeneous connections in dimension two. (English) Zbl 1372.53016

The author considers a problem of metrizability of locally homogeneous affine connections on 2-dimensional manifolds. Using the results from the papers [T. Arias-Marco and O. Kowalski, Monatsh. Math. 153, No. 1, 1–18 (2008; Zbl 1155.53009); O. Kowalski et al., Cent. Eur. J. Math. 2, No. 1, 87–102 (2004; Zbl 1060.53013); the author, Arch. Math., Brno 49, No. 5, 347–357 (2013; Zbl 1313.53021); the author and P. Žáčková, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 48, 157–170 (2009; Zbl 1195.53023)], she gives a few particular contributions relating metrizability of these connections to the Lie algebra of vector fields.

MSC:

53B05 Linear and affine connections
53B20 Local Riemannian geometry
PDF BibTeX XML Cite
Full Text: Link

References:

[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. | | · Zbl 1155.53009
[2] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry I, II. Wiley-Intersc. Publ., New York, Chichester, Brisbane, Toronto, Singapore, 1991. · Zbl 0119.37502
[3] Kowalski, O., Opozda, B., Vlášek, Z.: Curvature homogeneity of affine connections on two-dimensional manifolds. Coll. Math. 81, 1 (1999), 123-139. | · Zbl 0942.53019
[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. | | · Zbl 0993.53008
[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. · Zbl 1060.53013
[6] Mikeš, J., Stepanova, E., Vanžurová, A.: Differential Geometry of Special Mappings. Palacký University, Olomouc, 2015. | · Zbl 1337.53001
[7] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. Palacký University, Olomouc, 2009. | · Zbl 1222.53002
[8] Olver, P. J.: Equivalence, Invariants and Symmetry. Cambridge Univ. Press, Cambridge, 1995. | · Zbl 0837.58001
[9] Opozda, B.: A classification of locally homogeneous connections on 2-dimensional manifolds. Diff. Geom. Appl. 21 (2004), 173-198. | | · Zbl 1063.53024
[10] Singer, I. M.: Infinitesimally homogeneous spaces. Comm. Pure Appl. Math. 13 (1960), 685-697. | | · Zbl 0171.42503
[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. | · Zbl 1195.53023
[13] Vanžurová, A.: On metrizability of locally homogeneous affine connections on 2-dimensional manifolds. Arch. Math. (Brno) 49 (2013), 199-209.
[14] Vanžurová, A.: On metrizability of a class of 2-manifolds with linear connection. Miskolc Math. Notes 14, 3 (2013), 311-317. | · Zbl 1299.53034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.