This thesis concerns deformations of maps into submanifolds of projective spaces and in par- ticular the deformable surfaces of Lie sphere geometry. Using a gauge theoretic approach we study the transformations of Lie applicable surfaces and characterise certain classes of surfaces in terms of polynomial conserved quantities. In particular we unify isothermic, Guichard and L-isothermic surfaces as certain Lie applicable surfaces and show how their well known trans- formations arise in this setting. Another class of surfaces that is highlighted in this thesis is that of linear Weingarten surfaces in space forms and their transformations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:648954 |
| Date | January 2015 |
| Creators | Pember, Mason James Wyndham |
| Contributors | Burstall, Francis |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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