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The Pontryagin Forms of Hessian Manifolds

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

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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References

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Author information

Authors and Affiliations

  1. King’s College London, London, WC2R 2LS, UK

    J. Armstrong

  2. RIKEN Brain Science Institute, Saitama, 351-0198, Japan

    S. Amari

Authors
  1. J. Armstrong
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  2. S. Amari
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Corresponding author

Correspondence to J. Armstrong .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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© 2015 Springer International Publishing Switzerland

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Armstrong, J., Amari, S. (2015). The Pontryagin Forms of Hessian Manifolds. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_27

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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