Fiber-wise linear F-manifolds, compatible flat connections and Euler fields

Liana David

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arXiv · 2508.00474

Fiber-wise linear F-manifolds, compatible flat connections and Euler fields

Liana David

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Abstract

We define a fiber-wise linear (shortly, FWL) F-manifold as an F-manifold on the total space of a vector bundle \pi : E \rightarrow M for which the multiplication and unit field are FWL tensor fields. We develop a duality between FWL F-manifolds on E and the total space E^{*} of the dual vector bundle and we enrich it with FWL Euler fields and FWL compatible connections. We present examples in dimension two and three. We construct prolongations of F-manifolds and we prove that if the initial F-manifold admits a suitable Euler field or compatible flat connection then all prolongations inherit FWL Euler fields and FWL compatible flat connections.

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BibTeX RIS

Liana David. 2025-08-01. Fiber-wise linear F-manifolds, compatible flat connections and Euler fields. https://arxiv.org/abs/2508.00474

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