Frobenius 3-Folds via Singular Flat 3-Webs

Abstract

We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the Chern connection form is holomorphic, 3) the curvature form vanishes identically.

Keywords

• Frobenius manifold
• hexagonal 3-web
• Chern connection
• infinitesimal symmetry