Darboux and Calapso transforms of meromorphically isothermic surfaces
Abstract
We consider those simply connected isothermic surfaces for which their Hopf differential factorizes into a real function and a meromorphic quadratic differential that has a zero or pole at some point, but is nowhere zero and holomorphic otherwise. Upon restriction to a simply connected patch that does not contain the zero or pole, the Darboux and Calapso transformations yield new isothermic surfaces. We determine the limiting behaviour of these transformed patches as the zero or pole of the meromorphic quadratic differential is approached and investigate whether they are continuous around that point.
 Publication:

arXiv eprints
 Pub Date:
 January 2019
 arXiv:
 arXiv:1901.05774
 Bibcode:
 2019arXiv190105774F
 Keywords:

 Mathematics  Differential Geometry;
 35B40;
 51B10;
 58K10;
 58J72
 EPrint:
 27 pages, 4 figures