Natural Frobenius Submanifolds

Frobenius Manifolds as a Special Class of Submanifolds in Pseudo-Euclidean Spaces

We introduce a class of potential submanifolds in pseudo-Euclidean spaces (each N-dimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanifold. We show that all potential submanifolds bear natural special structures of Frobenius algebras on their tangent spaces. These special Frobenius structures are generated by the corresponding flat first fundamental form and the set of the second fundamental forms of the submani…

Realization of Frobenius manifolds as submanifolds in pseudo-Euclidean spaces

We introduce a class of k-potential submanifolds in pseudo-Euclidean spaces and prove that for an arbitrary positive integer k and an arbitrary nonnegative integer p, each N-dimensional Frobenius manifold can always be locally realized as an N-dimensional k-potential submanifold in ((k + 1) N + p)-dimensional pseudo-Euclidean spaces of certain signatures. For k = 1 this construction was proposed by the present author in a previous paper (2006). The realization of concrete Frobenius manifolds is reduced to solving a consistent linear system of second-order partial differential equations.

De Rham cohomology and homotopy Frobenius manifolds

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

余维2接触子流形的同调不变量

Homological invariants of codimension 2 contact submanifolds

本文构造余维2接触子流形的新同调不变量，将其刻画为环境接触同调代数的形变，并用于区分形式同痕而非接触同痕的嵌入及阻碍相关辛与Lagrangian配边。