Thomas Cecil is a math professor with an unrivalled snatch of Lie Sphere Geometry. right here, he presents a transparent and accomplished glossy remedy of the topic, in addition to its purposes to the learn of Euclidean submanifolds. It starts with the development of the distance of spheres, together with the elemental notions of orientated touch, parabolic pencils of spheres, and Lie sphere modifications. This new version includes revised sections on taut submanifolds, compact right Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. thoroughly new fabric on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with 3 and 4 significant curvatures is additionally incorporated. the writer surveys the identified leads to those fields and exhibits instructions for extra study and wider software of the equipment of Lie sphere geometry.
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