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.
Cite
CITATION STYLE
APA
Armstrong, J., & Amari, S. (2015). The pontryagin forms of hessian manifolds. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 240–247). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_27
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