On the local moduli space of locally homogeneous affine connections in plane domains

Oldřich Kowalski; Zdeněk Vlášek

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 2, page 229-234
  • ISSN: 0010-2628

Abstract

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Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [5] and [7] for two different versions of the solution.) Using a basic formula by B. Opozda, [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).

How to cite

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Kowalski, Oldřich, and Vlášek, Zdeněk. "On the local moduli space of locally homogeneous affine connections in plane domains." Commentationes Mathematicae Universitatis Carolinae 44.2 (2003): 229-234. <http://eudml.org/doc/249174>.

@article{Kowalski2003,
abstract = {Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [5] and [7] for two different versions of the solution.) Using a basic formula by B. Opozda, [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).},
author = {Kowalski, Oldřich, Vlášek, Zdeněk},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {two-dimensional manifolds with affine connection; locally homogeneous connections; two-dimensional manifolds with affine connection; locally homogeneous connections},
language = {eng},
number = {2},
pages = {229-234},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the local moduli space of locally homogeneous affine connections in plane domains},
url = {http://eudml.org/doc/249174},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Kowalski, Oldřich
AU - Vlášek, Zdeněk
TI - On the local moduli space of locally homogeneous affine connections in plane domains
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 2
SP - 229
EP - 234
AB - Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [5] and [7] for two different versions of the solution.) Using a basic formula by B. Opozda, [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).
LA - eng
KW - two-dimensional manifolds with affine connection; locally homogeneous connections; two-dimensional manifolds with affine connection; locally homogeneous connections
UR - http://eudml.org/doc/249174
ER -

References

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  1. Kobayashi S., Transformation Groups in Differential Geometry, Springer-Verlag, New York (1972). (1972) Zbl0246.53031MR0355886
  2. Kobayashi S., Nomizu K., Foundations of Differential Geometry I, Interscience Publ., New York (1963). (1963) Zbl0119.37502MR0152974
  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). (1999) MR1716190
  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). (2000) MR1767180
  5. Kowalski O., Opozda B., Vlášek Z., A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach, to appear. MR2041671
  6. Nomizu K., Sasaki T., Affine Differential Geometry, Cambridge University Press. Zbl1140.53001MR1311248
  7. Opozda B., Classification of locally homogeneous connections on 2-dimensional manifolds, preprint, 2002. Zbl1063.53024

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