A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach. (English) Zbl 1060.53013

P. J. Olver [Equivalences, Invariants and Symmetry (Cambridge University Press, Cambridge) (1995; Zbl 0837.58001)] classified all non-equivalent transitive Lie algebras of vector fields in \(\mathbb R^2\). In the present paper, the authors locally classify all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical approach. Namely, for each specific transitive algebra \(A\) of vector fields from Olver’s classification, the authors look for all affine connections for which A is an affine Killing algebra. Olver’s tables are presented at the end of the paper. A remark: the authors used the software Maple V Release 4.


53B05 Linear and affine connections
53C30 Differential geometry of homogeneous manifolds


Zbl 0837.58001


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