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We study an analogue of the classical Bianchi-Darboux transformation forL-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation.We show how to construct the Bianchi-Darboux transforms of an L-isothermicsurface by solving an integrable linear differential system. We then establisha permutability theorem for iterated Bianchi-Darboux transforms.

THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES