2 problems

Symmetry conjecture for the canonical divergence. The condition above together with $\nabla\,\mathcal{R}\equiv 0$ is sufficient for

Let $({\rm g},\nabla,\nabla^*)$ be a dualistic structure, with canonical divergences $\mathcal{D}(p,q)$ and $\mathcal{D}^*(p,q)$ and pseudo-squared-distance $r(p,q)$. Canonical-div…