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On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
Інший ID:
2010 Mathematics Subject Classification: 35Q51; 53A05; 22E70
DOI:10.3842/SIGMA.2015.046
DOI:10.3842/SIGMA.2015.046
Посилання:
On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces / S. Bertrand, A.M. Grundland, A.J. Hariton // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
We thank professor D. Levi (University of Roma Tre) for useful discussions on this topic. AMG’s
work was supported by a research grant from NSERC. SB acknowledges a doctoral fellowship
provided by the FQRNT of the Gouvernement du Qu´ebec. AJH wishes to acknowledge and
thank the Mathematical Physics Laboratory of the Centre de Recherches Math´ematiques for
the opportunity to contribute to this research.
Дата:
2015
Переглядів:
464
Завантажень:
240
Анотація:
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.
