How many Ricci flat affine connections are there with arbitrary torsion?

Abstrakt

In a previous paper, we solved the question how many real analytic connections with torsion exist locally in dimension n. In the present paper, we solve the questions how many of these connections are Ricci flat.

This family of affine connections is described in terms of the number of arbitrary functions of n variables. Suprisingly, the condition "Ricci flat" is not too restrictive when the dimension n is approaching to infinity.

Klíčová slova

• affine connection
• Ricci tensor
• Cauchy-Kowalevski Theorem