On Hessian Riemannian structures

Abstract

In Proposition 4.1 a characterization is given of Hessian Riemannian structures in terms of a natural connection in the general linear group GL(n; R) + , which is viewed as a principal SO(n)-bundle over the space of positive denite symmetric n n-matrices. For n = 2, Proposition 5.3 contains an interpretation of the curvature of a Hessian Riemannian structure at a given point, in terms of an umbilic point of a related surface in R 3 .