Abstract
Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic and Guichard surfaces of conformal geometry and L-isothermic surfaces of Laguerre geometry. In this setting one can see that the well known transformations available for these surfaces are induced by the transformations of the underlying Lie applicable surfaces. We also consider linear Weingarten surfaces in this setting and develop a new Bäcklund-type transformation for these surfaces.
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Acknowledgements
Open access funding provided by Austrian Science Fund (FWF). We would like to thank G. Szewieczek for reading through this paper and providing many useful comments. This work has been partially supported by the Austrian Science Fund (FWF) through the research project P28427-N35 “Non-rigidity and Symmetry breaking” as well as by FWF and the Japan Society for the Promotion of Science (JSPS) through the FWF/JSPS Joint Project Grant I1671-N26 “Transformations and Singularities”. The fourth author was also supported by the two JSPS grants Grant-in-Aid for Scientific Research (C) 15K04845 and (S) 24224001 (PI: M.-H. Saito).
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Burstall, F.E., Hertrich-Jeromin, U., Pember, M. et al. Polynomial conserved quantities of Lie applicable surfaces. manuscripta math. 158, 505–546 (2019). https://doi.org/10.1007/s00229-018-1033-0
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DOI: https://doi.org/10.1007/s00229-018-1033-0