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

2021/04/19 by Arsie, Alessandro, Buryak, Alexandr, Lorenzoni, Paolo +1 · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2104.09380

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.

Cited by

• Dubrovin duality for open Hurwitz flat F-manifolds
• F-manifolds, F_man-algebras and Poisson-algebra Distributions

Related

• Flat pencils of metrics and Frobenius manifolds
• F-manifolds with flat structure and Dubrovin's duality
• Bi-flat F-structures as differential bicomplexes and Gauss-Manin connections
• Riemannian manifolds with geometric structures
• Flat degenerate metrics and Riemannian foliations