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This œuvre, The Pontryagin Forms of Hessian Manifolds, by Shun-ichi Amari is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

The Pontryagin Forms of Hessian Manifolds


The Pontryagin Forms of Hessian Manifolds
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We show that Hessian manifolds of dimensions 4 and above must have vanishing Pontryagin forms. This gives a topological obstruction to the existence of Hessian metrics. We find an additional explicit curvature identity for Hessian 4-manifolds. By contrast, we show that all analytic Riemannian 2-manifolds are Hessian.
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The Pontryagin Forms of Hessian Manifolds
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