How many are affine connections with torsion

Abstract

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

Keywords

• Affine connections
• Ricci tensor
• Cauchy-Kowalewski Theorem