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SIGMA 8 (2012), 078, 15 pages arXiv:1206.0372
https://doi.org/10.3842/SIGMA.2012.078
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”
Frobenius 3-Folds via Singular Flat 3-Webs
Sergey I. Agafonov
Departmento de Matemática, Universidade Federal da Paraiba, João Pessoa, Brazil
Received May 28, 2012, in final form October 17, 2012; Published online October 21, 2012
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.
Key words:
Frobenius manifold; hexagonal 3-web; Chern connection; infinitesimal symmetry.
pdf (492 kb)
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