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- W2963229211 abstract "We study the limiting behaviour of Darboux and Calapso transforms of polarized curves in the conformal n-dimensional sphere when the polarization has a pole of first or second order at some point. We prove that for a pole of first order, as the singularity is approached, all Darboux transforms converge to the original curve and all Calapso transforms converge. For a pole of second order, a generic Darboux transform converges to the original curve while a Calapso transform has a limit point or a limit circle, depending on the value of the transformation parameter. In particular, our results apply to Darboux and Calapso transforms of isothermic surfaces when a singular umbilic with index $$frac{1}{2}$$ or 1 is approached along a curvature line." @default.
- W2963229211 created "2019-07-30" @default.
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- W2963229211 date "2018-11-19" @default.
- W2963229211 modified "2023-10-03" @default.
- W2963229211 title "Transformations and singularities of polarized curves" @default.
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- W2963229211 doi "https://doi.org/10.1007/s10455-018-9639-8" @default.
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