| Title:
|
On the local moduli space of locally homogeneous affine connections in plane domains (English) |
| Author:
|
Kowalski, Oldřich |
| Author:
|
Vlášek, Zdeněk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
229-234 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See \cite{5} and \cite{7} for two different versions of the solution.) Using a basic formula by B. Opozda, \cite{7}, we prove that all locally homogeneous torsion-less affine connections defined in open domains of a 2-dimensional manifold depend essentially on at most 4 parameters (see Theorem 2.4). (English) |
| Keyword:
|
two-dimensional manifolds with affine connection |
| Keyword:
|
locally homogeneous connections |
| MSC:
|
53B05 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1097.53009 |
| idMR:
|
MR2026160 |
| . |
| Date available:
|
2009-01-08T19:28:58Z |
| Last updated:
|
2020-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119382 |
| . |
| Reference:
|
[1] Kobayashi S.: Transformation Groups in Differential Geometry.Springer-Verlag, New York (1972). Zbl 0246.53031, MR 0355886 |
| Reference:
|
[2] Kobayashi S., Nomizu K.: Foundations of Differential Geometry I.Interscience Publ., New York (1963). Zbl 0119.37502, MR 0152974 |
| Reference:
|
[3] Kowalski O., Opozda B., Vlášek Z.: Curvature homogeneity of affine connections on two-dimensional manifolds.Colloq. Math., ISSN 0010-1354, 81 1 123-139 (1999). MR 1716190 |
| Reference:
|
[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., ISSN 0026-9255, 130 Springer-Verlag, Wien 109-125 (2000). MR 1767180 |
| Reference:
|
[5] Kowalski O., Opozda B., Vlášek Z.: A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach.to appear. MR 2041671 |
| Reference:
|
[6] Nomizu K., Sasaki T.: Affine Differential Geometry.Cambridge University Press. Zbl 1140.53001, MR 1311248 |
| Reference:
|
[7] Opozda B.: Classification of locally homogeneous connections on 2-dimensional manifolds.preprint, 2002. Zbl 1063.53024 |
| . |
