A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach
type: Item
instance of: scholarly article
title: A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach
zbMATH Open document ID: 1060.53013
DOI: 10.2478/BF02475953
author: Oldřich Kowalski
author: Barbara Opozda
author: Zdeněk Vlášek
published in: Central European Journal of Mathematics
publication date: 2004-02-23T00:00:00Z
review text: \textit{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.
reviewed by: Valentin Boju
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 2046456
zbMATH Keywords: two-dimensional manifolds with affine connection
zbMATH Keywords: locally homogeneous connections
zbMATH Keywords: Lie algebras of vector fields
zbMATH Keywords: Killing vector fields
zbMATH Keywords: Olver's classification
zbMATH Keywords: Opozda's formula
zbMATH Keywords: software Maple V Release 4
describes a project that uses: Maple
MaRDI profile type: Publication
cites work: Q5658761
cites work: Q5731354
cites work: Curvature homogeneity of affine connections on two-dimensional manifolds
cites work: A classification of locally homogeneous affine connections with skew-symmetric Ricci tensor on 2-dimensional manifolds
cites work: Q5488105
cites work: Q4846450
cites work: Q4849745
cites work: A classification of locally homogeneous connections on 2-dimensional manifolds
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description: scientific article; zbMATH DE number 2046456