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Symmetric affine surfaces with torsion. (English) Zbl 1430.53048

Summary: 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.

MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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