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

Symmetry Integrability and Geometry-Methods and Applications

article

Sébastien Bertrand¹  Alfred M. Grundland²  Alexander J. Hariton³ 

[1] Department of Mathematics and Statistics, Université de Montréal;Department of Mathematics and Computer Science;Centre de Recherches Mathématiques, Université de Montréal

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

DOI  :  10.3842/SIGMA.2015.046

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown