The Pontryagin Forms of Hessian Manifolds

  • J. ArmstrongEmail author
  • S. Amari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)


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.


Riemannian Metrics Symmetric Power Flat Structure Flat Connection Topological Obstruction 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.King’s College LondonLondonUK
  2. 2.RIKEN Brain Science InstituteSaitamaJapan

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