Curvature of Hessian Manfiolds
Differential Geometry
2013-12-05 v1
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.
Keywords
Cite
@article{arxiv.1312.1103,
title = {Curvature of Hessian Manfiolds},
author = {Shun-ichi Amari and John Armstrong},
journal= {arXiv preprint arXiv:1312.1103},
year = {2013}
}
Comments
18 pages