Special surface classes

Abstract

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 Award	5 May 2015
Original language	English
Awarding Institution	University of Bath
Supervisor	Fran Burstall (Supervisor)