Iterated Darboux Transformation for Isothermic Surfaces in Terms of Clifford Numbers
Keyword(s):
Isothermic surfaces are defined as immersions with the curvture lines admitting conformal parameterization. We present and discuss the reconstruction of the iterated Darboux transformation using Clifford numbers instead of matrices. In particulalr, we derive a symmetric formula for the two-fold Darboux transformation, explicitly showing Bianchi’s permutability theorem. In algebraic calculations an important role is played by the main anti-automorphism (reversion) of the Clifford algebra C(4,1) and the spinorial norm in the corresponding Spin group.
2000 ◽
Vol 11
(07)
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pp. 911-924
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2016 ◽
Vol 42
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pp. 73-94
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2012 ◽
Vol 56
(1)
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pp. 67-78
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2003 ◽
Vol 2003
(49)
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pp. 3123-3142
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