Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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.

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References

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