Before revision:  Using the tools of information geometry and optimal transport, we show that L-divergence induces a new information geometry on the simplex . This geometric structure consists of a Riemannian metric and a pair of dually coupled affine connections defining two kinds of geodesics.
After revision:  Using the tools of information geometry and optimal transport, we show that L-divergence induces a new information geometry on the simplex consisting of a Riemannian metric and a pair of dually coupled affine connections defining two kinds of geodesics.