Curvature homogeneity of affine connections on two-dimensional manifolds

• Autorzy: Oldřich Kowalski , Barbara Opozda , Zdeněk Vlášek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 81
• Numer: 1
• Strony: 123-139

Daty

wydano

1999

otrzymano

1998-06-26

poprawiono

1999-02-08

Twórcy

autor

Oldřich Kowalski

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic

autor

Barbara Opozda

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

autor

Zdeněk Vlášek

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic

Bibliografia

• [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.