Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 046, 16 pages      arXiv:1502.02948      https://doi.org/10.3842/SIGMA.2015.046
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet

On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces

Sébastien Bertrand a, Alfred M. Grundland bc and Alexander J. Hariton c
a) Department of Mathematics and Statistics, Université de Montréal, Montréal CP 6128 (QC) H3C 3J7, Canada
b) Department of Mathematics and Computer Science, Université du Québec, Trois-Rivières, CP 500 (QC) G9A 5H7, Canada
c) Centre de Recherches Mathématiques, Université de Montréal, Montréal CP 6128 (QC) H3C 3J7, Canada

Received February 11, 2015, in final form June 09, 2015; Published online June 17, 2015

Abstract
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of the symmetry properties of both the classical and supersymmetric versions of the Gauss-Weingarten equations is performed. A supersymmetric generalization of the conjecture establishing the necessary conditions for a system to be integrable in the sense of soliton theory is formulated and illustrated by the examples of supersymmetric versions of the sine-Gordon equation and the Gauss-Codazzi equations.

Key words: supersymmetric models; Lie superalgebras; symmetry reduction; conformally parametrized surfaces; integrability.

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