Curvature of Hessian manifolds

S Amari,J Armstrong

doi:10.1016/j.difgeo.2014.01.001

Curvature of Hessian manifolds

S Amari, J Armstrong

Open Access

https://doi.org/10.1016/j.difgeo.2014.01.001

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Journal: Differential Geometry and its Applications	Publication Date: Jan 29, 2014
Citations: 37	License type: publisher-specific-oa

Affiliation: King's College London

#Hessian Metrics #Hessian Manifold + Show 5 more

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Abstract

We prove that, in dimensions greater than 2, the generic metric is not a Hessian metric and find a curvature condition on Hessian metrics in dimensions greater than 3. In particular we prove that the forms used to define the Pontryagin classes in terms of the curvature vanish on a Hessian manifold. By contrast all analytic Riemannian 2-metrics are Hessian metrics.

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