Special surface classes

Student thesis: Doctoral ThesisPhD


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.
Date of Award5 May 2015
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorFran Burstall (Supervisor)

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