Symmetric affine surfaces with torsion

D'ASCANIO, D.; GILKEY, P.B.; PISANI, P.

JOURNAL OF GEOMETRY AND PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2019 vol. 147 p. 103536 - 103545

0393-0440

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.