How many are equiaffine connections with torsion

Abstract

The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold M of dimension n is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.

Keywords

• Equiaffine connections with torsion
• Ricci tensor