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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