A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

Oldřich Kowalski; Barbara Opozda; Zdeněk Vlášek

Open Mathematics (2004)

  • Volume: 2, Issue: 1, page 87-102
  • ISSN: 2391-5455

Abstract

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The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].

How to cite

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Oldřich Kowalski, Barbara Opozda, and Zdeněk Vlášek. "A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach." Open Mathematics 2.1 (2004): 87-102. <http://eudml.org/doc/268829>.

@article{OldřichKowalski2004,
abstract = {The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].},
author = {Oldřich Kowalski, Barbara Opozda, Zdeněk Vlášek},
journal = {Open Mathematics},
keywords = {53B05; 53C30},
language = {eng},
number = {1},
pages = {87-102},
title = {A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach},
url = {http://eudml.org/doc/268829},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Oldřich Kowalski
AU - Barbara Opozda
AU - Zdeněk Vlášek
TI - A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach
JO - Open Mathematics
PY - 2004
VL - 2
IS - 1
SP - 87
EP - 102
AB - The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].
LA - eng
KW - 53B05; 53C30
UR - http://eudml.org/doc/268829
ER -

References

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  1. [1] S. Kobayashi: Transformation Groups in Differential Geometry, Springer-Verlag, New York, 1972. Zbl0246.53031
  2. [2] S. Kobayashi, K. Nomizu: Foundations of Differential Geometry I, Interscience Publ., New York, 1963. 
  3. [3] O. Kowalski, B. Opozda, Z. Vlášek: “Curvature homogeneity of affine connections on two-dimensional manifolds”, Colloquium Mathematicum, Vol. 81, (1999), pp. 123–139. Zbl0942.53019
  4. [4] O. Kowalski, B. Opozda, Z. Vlášek: “A classification of locally homogeneous affine connections with skew-symmetric Ricci tensor on 2-dimensional manifolds”, Monatshefte für Mathematik, (2000), pp. 109–125. Zbl0993.53008
  5. [5] O. Kowalski, Z. Vlášek: “On the local moduli space of locally homogeneous affine connections in plane domains”, Comment. Math. Univ. Carolinae, (2003), pp. 229–234. Zbl1097.53009
  6. [6] K. Nomizu, T. Sasaki: Affine Differential Geometry, Cambridge University Press, Cambridge, 1994. 
  7. [7] P.J. Olver: Equivalence, Invariants and Symmetry Cambridge University Press, Cambridge, 1995. 
  8. [8] B. Opozda: “Classification of locally homogeneous connections on 2-dimensional manifolds”, to appear in Diff. Geom. Appl.. 

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