3-dimensional F-manifolds

TL;DR

This paper classifies 3-dimensional F-manifolds, which are complex manifolds with a special multiplication structure, providing insights into their local structure with or without Euler fields.

Contribution

It offers a comprehensive local classification of 3-dimensional F-manifolds, expanding understanding of their structure and properties.

Findings

Classification of 3-dimensional F-manifolds achieved

Distinction between manifolds with and without Euler fields clarified

Structural properties of these manifolds elucidated

Abstract

F-manifolds are complex manifolds with a multiplication with unit on the holomorphic tangent bundle with a certain integrability condition. Here the local classification of 3-dimensional F-manifolds with or without Euler fields is pursued.