| Title:
|
On Metrizable Locally Homogeneous Connections in Dimension (English) |
| Author:
|
Vanžurová, Alena |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
157-166 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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.]. (English) |
| Keyword:
|
Manifold |
| Keyword:
|
affine connection |
| Keyword:
|
Riemannian connection |
| Keyword:
|
Lorentzian connection |
| Keyword:
|
Killing vector field |
| Keyword:
|
locally homogeneous space |
| MSC:
|
53B05 |
| MSC:
|
53B20 |
| idZBL:
|
Zbl 1372.53016 |
| idMR:
|
MR3674609 |
| . |
| Date available:
|
2016-08-30T12:08:08Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145826 |
| . |
| Reference:
|
[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, MR 2366132, 10.1007/s00605-007-0494-0 |
| Reference:
|
[2] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry I, II.. Wiley-Intersc. Publ., New York, Chichester, Brisbane, Toronto, Singapore, 1991. |
| Reference:
|
[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, MR 1716190, 10.4064/cm-81-1-123-139 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations.. Palacký University, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[8] Olver, P. J.: Equivalence, Invariants and Symmetry.. Cambridge Univ. Press, Cambridge, 1995. Zbl 0837.58001, MR 1337276 |
| Reference:
|
[9] Opozda, B.: A classification of locally homogeneous connections on 2-dimensional manifolds.. Diff. Geom. Appl. 21 (2004), 173–198. Zbl 1063.53024, MR 2073824, 10.1016/j.difgeo.2004.03.005 |
| Reference:
|
[10] Singer, I. M.: Infinitesimally homogeneous spaces.. Comm. Pure Appl. Math. 13 (1960), 685–697. Zbl 0171.42503, MR 0131248, 10.1002/cpa.3160130408 |
| Reference:
|
[11] Vanžurová, A., Žáčková, P.: Metrization of linear connections.. Aplimat, J. of Applied Math. (Bratislava) 2, 1 (2009), 151–163. |
| Reference:
|
[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, MR 2641956 |
| Reference:
|
[13] Vanžurová, A.: On metrizability of locally homogeneous affine connections on 2-dimensional manifolds.. Arch. Math. (Brno) 49 (2013), 199–209. MR 3159333 |
| Reference:
|
[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, MR 3144100 |
| . |
