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 Tr. Mat. Inst. Steklova, 2009, Volume 267, Pages 226–244 (Mi tm2588)

Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces

O. I. Mokhovab

a Department of Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Centre for Nonlinear Studies, L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia

Abstract: 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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 267, 217–234

Bibliographic databases:

UDC: 514.7+514.8+517.958+517.95+512.55

Citation: O. I. Mokhov, “Realization of Frobenius Manifolds as Submanifolds in Pseudo-Euclidean Spaces”, Singularities and applications, Collected papers, Tr. Mat. Inst. Steklova, 267, MAIK Nauka/Interperiodica, Moscow, 2009, 226–244; Proc. Steklov Inst. Math., 267 (2009), 217–234

Citation in format AMSBIB
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This publication is cited in the following articles:
1. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
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