Riemannian curvature of gaussian distribution in dual coordinate system

Abstract: In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this new coordinate system, which allows us to characterize existing geometric invariants, such as the dual potential function and the Fisher metric.