Geodesic
Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces
Informatics and Automation, Singularities and applications, Tome 267 (2009), pp. 226-244

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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. 
@article{TRSPY_2009_267_a17,
     author = {O. I. Mokhov},
     title = {Realization of {Frobenius} {Manifolds} as {Submanifolds} in {Pseudo-Euclidean} {Spaces}},
     journal = {Informatics and Automation},
     pages = {226--244},
     publisher = {mathdoc},
     volume = {267},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_267_a17/}
}
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O. I. Mokhov. Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces. Informatics and Automation, Singularities and applications, Tome 267 (2009), pp. 226-244. http://geodesic.mathdoc.fr/item/TRSPY_2009_267_a17/