×

zbMATH — the first resource for mathematics

A classification of locally homogeneous connections on 2-dimensional manifolds. (English) Zbl 1063.53024
In this very interesting paper, the author classifies (in appropriate coordinate systems) all torsion-free locally homogeneous connections on 2-dimensional manifolds: Levi-Civita connections of metrics with constant curvature; connections with constant coefficients; connections of a special type, with a kind of asymptotic flatness of the coefficients.

MSC:
53C05 Connections (general theory)
53C30 Differential geometry of homogeneous manifolds
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Nomizu, K.; Sasaki, T., Affine differential geometry, (1994), Cambridge University Press Cambridge · Zbl 0834.53002
[2] Kowalski, O.; Opozda, B.; Vlášek, Z., Curvature homogeneity of affine connections on two-dimensional manifolds, Colloq. math., 81, 123-139, (1999) · Zbl 0942.53019
[3] Kowalski, O.; Opozda, B.; Vlášek, Z., A classification of locally homogeneous connections with skew-symmetric Ricci tensor on 2-dimensional manifolds, Monatsh. math., 130, 109-125, (2000) · Zbl 0993.53008
[4] O. Kowalski, B. Opozda, Z. Vlášek, A classification of locally homogeneous affine connections on 2-dimensional manifolds via group-theoretical approach, CEJM, submitted for publication
[5] Kowalski, O.; Opozda, B.; Vlášek, Z., On locally non-homogeneous pseudo-Riemannian manifolds with locally homogeneous Levi-Civita connections, Internat. J. math., 14, 559-572, (2003) · Zbl 1061.53049
[6] Kowalski, O.; Vlášek, Z., On the moduli space on locally homogeneous affine connections in plane domains, Comment. math. univ. carolinae, 44, 229-234, (2003) · Zbl 1097.53009
[7] Olver, P.J., Equivalence, invariants and symmetry, (1995), Cambridge University Press Cambridge · Zbl 0837.58001
[8] Opozda, B., On curvature homogeneous and locally homogeneous affine connections, Proc. amer. math. soc., 124, 1889-1893, (1996) · Zbl 0864.53013
[9] Opozda, B., Affine versions of Singer’s theorem on locally homogeneous spaces, Ann. global. anal. geom., 15, 187-199, (1997) · Zbl 0881.53010
[10] B. Opozda, Locally homogeneous affine connections on compact surfaces, Proc. Amer. Math. Soc., submitted for publication · Zbl 1057.53018
[11] Singer, I.M., Infinitesimally homogeneous spaces, Comm. pure appl. math., 13, 685-697, (1960) · Zbl 0171.42503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.