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Integrable graded manifolds and nonlinear equations

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Abstract

A method is proposed for the classification of integrable embeddings of (2+2)-dimensional supermanifoldsV 2|2 into an enveloping superspace supplied with the structure of a Lie superalgebra. The approach is first applied to the “even part” of the scheme, i.e. for the embeddings of 2-dimensional manifoldsV 2 into Riemannian or non-Riemannian enveloping space. The general consideration is also illustrated by the example of superspaces supplied with the structure of the series sl(n, n+1), whose integrable supermanifolds are described by supersymmetrical 2-dimensional Toda lattice type equations. In particular, forn=1 they are described by the supersymmetrical Liouville and Sine-Gordon equations.

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Authors and Affiliations

  1. Institute for High Energy Physics, Protvino, Serpukhov, P.O. Box 35, SU-142284, Moscow Region, USSR

    M. V. Saveliev

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  1. M. V. Saveliev
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Communicated by Ya. G. Sinai

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Saveliev, M.V. Integrable graded manifolds and nonlinear equations. Commun.Math. Phys. 95, 199–216 (1984). https://doi.org/10.1007/BF01468141

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  • DOI: https://doi.org/10.1007/BF01468141

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