Curvature homogeneity of affine connections on two-dimensional manifolds

Oldřich Kowalski; Barbara Opozda; Zdeněk Vlášek

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 1, page 123-139
  • ISSN: 0010-1354

Abstract

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Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.

How to cite

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Kowalski, Oldřich, Opozda, Barbara, and Vlášek, Zdeněk. "Curvature homogeneity of affine connections on two-dimensional manifolds." Colloquium Mathematicae 81.1 (1999): 123-139. <http://eudml.org/doc/210723>.

@article{Kowalski1999,
abstract = {Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.},
author = {Kowalski, Oldřich, Opozda, Barbara, Vlášek, Zdeněk},
journal = {Colloquium Mathematicae},
keywords = {curvature homogeneous connections; two-dimensional manifolds with affine connection; locally homogeneous connections; curvature homogeneous connection; locally homogeneous connection},
language = {eng},
number = {1},
pages = {123-139},
title = {Curvature homogeneity of affine connections on two-dimensional manifolds},
url = {http://eudml.org/doc/210723},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Kowalski, Oldřich
AU - Opozda, Barbara
AU - Vlášek, Zdeněk
TI - Curvature homogeneity of affine connections on two-dimensional manifolds
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 1
SP - 123
EP - 139
AB - Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.
LA - eng
KW - curvature homogeneous connections; two-dimensional manifolds with affine connection; locally homogeneous connections; curvature homogeneous connection; locally homogeneous connection
UR - http://eudml.org/doc/210723
ER -

References

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  1. [1] E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, World Sci., 1996. Zbl0904.53006
  2. [2] P. Bueken and L. Vanhecke, Examples of curvature homogeneous Lorentz metrics, Classical Quantum Gravity 14 (1997), L93-L96. Zbl0882.53036
  3. [3] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry I, Interscience, New York, 1963. Zbl0119.37502
  4. [4] B. Opozda, On curvature homogeneous and locally homogeneous affine connections, Proc. Amer. Math. Soc. 124 (1996), 1889-1893. Zbl0864.53013
  5. [5] B. Opozda, Affine versions of Singer's Theorem on locally homogeneous spaces, Ann. Global Anal. Geom. 15 (1997), 187-199. Zbl0881.53010
  6. [6] I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. Zbl0171.42503

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