Frobenius submanifolds

Abstract

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.

23 pages. LaTeX 2e

References in corpus (4)

• Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
• Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
• Multiplication on the tangent bundle
• Jordan manifolds and dispersionless KdV equations

Cited by in corpus (14)

• On Associativity Equations in Dispersionless Integrable Hierarchies
• Frobenius Manifolds: Natural submanifolds and induced bi-Hamiltonian structures
• Local Moduli of Semisimple Frobenius Coalescent Structures
• Compatible metrics on a manifold and non-local bi-Hamiltonian structures
• Frobenius manifolds and a new class of extended affine Weyl groups ${\tilde{W}}^{(k,k+1)}(A_l)$
• Orbifold GW theory as Hurwitz-Frobenius submanifold
• Big quantum cohomology of Fano complete intersections
• The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$
• Isomonodromic deformations along a stratum of the coalescence locus
• Hypersurfaces with flat centroaffine metric and equations of associativity
• Formal Frobenius structures generated by geometric deformation algebras
• Natural Frobenius Submanifolds
• Infinite-dimensional Frobenius Manifolds Underlying the Universal Whitham Hierarchy
• Infinite-dimensional Frobenius Manifolds Underlying the Toda Lattice Hierarchy