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arXiv · 2104.09380

Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics

Alessandro Arsie·Alexandr Buryak·Paolo Lorenzoni·Paolo Rossi
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Abstract

In this paper we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold we present a construction of a canonical flat F-manifold associated to it. We also describe a construction of a canonical homogeneous Riemannian F-manifold associated to an arbitrary exact homogeneous flat pencil of metrics satisfying a certain non-degeneracy assumption. In the last part of the paper we construct Legendre transformations for Riemannian F-manifolds.

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Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni, Paolo Rossi. 2021-04-19. Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics. https://arxiv.org/abs/2104.09380

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