%0 Journal Article
%T Realization of Frobenius manifolds as submanifolds in pseudo-Euclidean spaces
%A O. I. Mokhov
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0911.4212v1