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

[摘要] 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.

[关键词] supersymmetric models;Lie superalgebras;symmetry reduction;conformally parametrized surfaces;integrability