We study an analogue of the classical Backlund transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. First we show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system, then we establish a permutability theorem for iterated Bianchi-Darboux transforms.
The Bianchi-Darboux transform of L-isothermic surfaces / Musso, E.; Nicolodi, Lorenzo. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 11:7(2000), pp. 911-924. [10.1142/S0129167X00000465]
The Bianchi-Darboux transform of L-isothermic surfaces
NICOLODI, Lorenzo
2000-01-01
Abstract
We study an analogue of the classical Backlund transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. First we show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system, then we establish a permutability theorem for iterated Bianchi-Darboux transforms.File in questo prodotto:
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