2014/12/15 by S Bertrand, A M Grundland, Bertrand, S +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Computer science #Extension (predicate logic) #FOS: Physical sciences #Gauss #Geometry #Homogeneous space #Lie superalgebra #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Superalgebra #Superfield #Superspace #Supersymmetry #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1412.4774
arxiv created 2014/12/15 · openalex publication_date 2014/12/15 · arxiv updated 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A fermionic supersymmetric extension is established for the Gauss-Weingarten and Gauss-Codazzi equations describing conformally parametrized surfaces immersed in a Grassmann superspace. An analysis of this extension is performed using a superspace-superfield formalism together with a supersymmetric version of a moving frame on a surface. In contrast with the bosonic supersymmetric extension, the equations of the fermionic supersymmetric Gauss-Codazzi model resemble the form of the classical equations. Next, a superalgebra of Lie point symmetries of these equations is determined and a classification of the one-dimensional subalgebras of this superalgebra into conjugacy classes is presented. The symmetry reduction method is used to obtain group-invariants, orbits and reduced systems for three chosen one-dimensional subalgebras. The explicit solutions of these reduced systems correspond to different surfaces immersed in a Grassmann superspace. Within this framework for the supersymmetric version of the Gauss-Codazzi equations a geometrical interpretation of the results is dicussed.