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dc.contributor.authorNoonan, Matthewen_US
dc.identifier.otherbibid: 7061582
dc.description.abstractA classical theorem of Bianchi states that two surfaces in space are the focal surfaces of a pseudospherical line congruence only if each surface has constant negative Gaussian curvature. Lie constructed a partial converse, explicitly calculating from one surface of constant negative curvature a pseudospherical line congruence and matching surface. We construct a generalization of these theorems to submanifolds of arbitrary homogeneous spaces. Applications are given to surfaces in the classical space forms and in a novel geometry related to the group of Lie sphere transformations.en_US
dc.titleGeometric Backlund Transformations In Homogeneous Spacesen_US
dc.typedissertation or thesisen_US

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