The Pontryagin Forms of Hessian Manifolds

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14280

Résumé

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.

The Pontryagin Forms of Hessian Manifolds

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application/pdf The Pontryagin Forms of Hessian Manifolds John Armstrong, Shun-Ichi Amari

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        <identifier identifierType="DOI">10.23723/11784/14280</identifier><creators><creator><creatorName>John Armstrong</creatorName></creator><creator><creatorName>Shun-Ichi Amari</creatorName></creator></creators><titles>
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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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