ArticleOriginal scientific text
Title
Curvature homogeneity of affine connections on two-dimensional manifolds
Authors 1, 2, 1
Affiliations
- Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic
- 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
- E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, World Sci., 1996.
- P. Bueken and L. Vanhecke, Examples of curvature homogeneous Lorentz metrics, Classical Quantum Gravity 14 (1997), L93-L96.
- S. Kobayashi and K. Nomizu, Foundations of Differential Geometry I, Interscience, New York, 1963.
- B. Opozda, On curvature homogeneous and locally homogeneous affine connections, Proc. Amer. Math. Soc. 124 (1996), 1889-1893.
- B. Opozda, Affine versions of Singer's Theorem on locally homogeneous spaces, Ann. Global Anal. Geom. 15 (1997), 187-199.
- I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697.