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arXiv · 1511.06637

Hermitian metrics on F-manifolds

Liana David·Claus Hertling
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Abstract

An $F$-manifold is complex manifold with a multiplication on the holomorphic tangent bundle with a certain integrability condition. Important examples are Frobenius manifolds and especially base spaces of universal unfoldings of isolated hypersurface singularities. This paper reviews the construction of hermitian metrics on $F$-manifolds from $tt^*$ geometry. It clarifies the logic between several notions. It also introduces a new {\it canonical} hermitian metric. Near irreducible points it makes the manifold almost hyperbolic. This holds for the singularity case and will hopefully lead to applications there.

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BibTeXRIS

Liana David, Claus Hertling. 2016-04-27. Hermitian metrics on F-manifolds. https://doi.org/10.1016/j.geomphys.2016.05.005

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