Standard divergence in manifold of dual affine connections

Abstract

A divergence function defines a Riemannian metric G and dually coupled affine connections (∇,∇∗) with respect to it in a manifold M. When M is dually flat, a canonical divergence is known, which is uniquely determined from {G,∇,∇∗}. We search for a standard divergence for a general non-flat M. It is introduced by the magnitude of the inverse exponential map, where α = −(1/3) connection plays a fundamental role. The standard divergence is different from the canonical divergence.