Lie Sphere Geometry

Professor Thomas E. Cecil is a professor of mathematics at Holy Cross University, where he has taught for almost thirty years. He has held visiting appointments at UC Berkeley, Brown University, and the University of Notre Dame. He has written several articles on Dupin submanifolds and hypersurfaces, and their connections to Lie sphere geometry, and co-edited two volumes on tight and taught submanifolds.

Reviews from the first edition: "The book under review sets out the basic material on Lie sphere geometry in modern notation, thus making it accessible to students and researchers in differential geometry...This is a carefully written, thorough, and very readable book. There is an excellent bibliography that not only provides pointers to proofs that have been omitted, but gives appropriate references for the results presented. It should be useful to all geometers working in the theory of submanifolds." - P.J. Ryan, MathSciNet "The book under review is an excellent monograph about Lie sphere geometry and its recent applications to the study of submanifolds of Euclidean space...The book is written in a very clear and precise style. It contains about a hundred references, many comments of and hints to the topical literature, and can be considered as a milestone in the recent development of a classical geometry, to which the author contributed essential results." - R. Sulanke, Zentralblatt

• Lie Sphere Geometry.- Lie Sphere Transformations.- Legendre Submanifolds.- Dupin Submanifolds.