Frobenius submanifolds

Details Frobenius submanifolds Frobenius submanifolds

1999-12-10

arxiv.org/abs/math/9912081v1

J.Geom.Phys. 38 (2001) 285-307

Mathematics

Differential Geometry

23 pages. LaTeX 2e

Scientific paper

The notion of a Frobenius submanifold - a submanifold of a Frobenius manifold which is itself a Frobenius manifold with respect to structures induced from the original manifold - is studied. Two dimensional submanifolds are particularly simple. More generally, sufficient conditions are given for a submanifold to be a so-called natural submanifold. These ideas are illustrated using examples of Frobenius manifolds constructed from Coxeter groups, and for the Frobenius manifolds governing the quantum cohomology of CP^2 and CP^1 \times CP^1.

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