Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 11-26 (2007)

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Classification of locally projectively homogeneous torsion-less affine connections in the plane domains

Oldrich Kowalski and Zdenek Vlásek

Charles University Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha, Czech Republic, e-mail: \quad

Abstract: The aim of this paper is to classify (locally) all torsion-less locally projectively homogeneous affine connections on 2-dimensional manifolds. Especially, we express, in a simple and explicit form, all such connections which are not projectively flat (Theorem 1). We make also some conclusions from this classification (Theorem 2 and Theorem3).

Keywords: two-dimensional manifolds with affine connection, projectively homogeneous connections, Lie algebras of vector fields, Killing vector fields

Classification (MSC2000): 53B05, 53C30

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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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