ArticleOriginal scientific text

Title

Curvature homogeneity of affine connections on two-dimensional manifolds

Authors 1, 2, 1

Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic
  2. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

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.

Keywords

curvature homogeneous connections, two-dimensional manifolds with affine connection, locally homogeneous connections

Bibliography

  1. E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, World Sci., 1996.
  2. P. Bueken and L. Vanhecke, Examples of curvature homogeneous Lorentz metrics, Classical Quantum Gravity 14 (1997), L93-L96.
  3. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry I, Interscience, New York, 1963.
  4. B. Opozda, On curvature homogeneous and locally homogeneous affine connections, Proc. Amer. Math. Soc. 124 (1996), 1889-1893.
  5. B. Opozda, Affine versions of Singer's Theorem on locally homogeneous spaces, Ann. Global Anal. Geom. 15 (1997), 187-199.
  6. I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697.
Pages:
123-139
Main language of publication
English
Received
1998-06-26
Accepted
1999-02-08
Published
1999
Exact and natural sciences