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

Sébastien Bertrand ; Alfred M. Grundland ; Alexander J. Hariton

Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)

Résumé

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.

Détail

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

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