paper

Symmetric affine surfaces with torsion

arXiv:1910.10028 · doi:10.1016/j.geomphys.2019.103536

Abstract

We study symmetric affine surfaces which have non-vanishing torsion tensor. We give a complete classification of the local geometries possible if the torsion is assumed parallel. This generalizes a previous result of Opozda in the torsion free setting; these geometries are all locally homogeneous. If the torsion is not parallel, we assume the underlying surface is locally homogeneous and provide a complete classification in this setting as well.

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