The Symmetry Group of Lamé's System and the Associated Guichard Nets for Conformally Flat Hypersurfaces
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Symmetry Group of Lamé's System and the Associated Guichard Nets for Conformally Flat Hypersurfaces
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| Creator |
dos Santos, J.P.
Tenenblat, K. |
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| Description |
We consider conformally flat hypersurfaces in four dimensional space forms with their associated Guichard nets and Lamé's system of equations. We show that the symmetry group of the Lamé's system, satisfying Guichard condition, is given by translations and dilations in the independent variables and dilations in the dependents variables. We obtain the solutions which are invariant under the action of the 2-dimensional subgroups of the symmetry group. For the solutions which are invariant under translations, we obtain the corresponding conformally flat hypersurfaces and we describe the corresponding Guichard nets. We show that the coordinate surfaces of the Guichard nets have constant Gaussian curvature, and the sum of the three curvatures is equal to zero. Moreover, the Guichard nets are foliated by flat surfaces with constant mean curvature. We prove that there are solutions of the Lamé's system, given in terms of Jacobi elliptic functions, which are invariant under translations, that correspond to a new class of conformally flat hypersurfaces.
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| Date |
2019-02-19T18:34:43Z
2019-02-19T18:34:43Z 2013 |
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| Type |
Article
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| Identifier |
The Symmetry Group of Lamé's System and the Associated Guichard Nets for Conformally Flat Hypersurfaces / J.P. dos Santos, K. Tenenblat // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 24 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53A35; 53C42 DOI: http://dx.doi.org/10.3842/SIGMA.2013.033 http://dspace.nbuv.gov.ua/handle/123456789/149203 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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