This article is cited in 2 papers

Frobenius 3-folds via singular flat 3-webs

Sergey I. Agafonov

Departmento de Matemática, Universidade Federal da Paraiba, João Pessoa, Brazil

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.

MSC: 53A60; 53D45; 34M35

Received: May 28, 2012; in final form October 17, 2012; Published online October 21, 2012

Language: English

DOI: 10.3842/SIGMA.2012.078

Bibliographic databases:

• 
• 
• 

ArXiv: 1206.0372