Geodesic submanifolds of a family of statistical models

Given the Riemannian manifold, determined by the Fisher information metric in the statistical model with location parameters induced by the family of probability density functions on : P[Omega] = {exp( - c([omega])x2 + [phi]([omega])x - [psi]([omega])): [omega] [epsilon] [Omega]} with c([omega]) > 0, for every [omega] [set membership, variant] [Omega], conditions are found for the level submanifolds to be geodesic.