Lie Sphere Geometry

With Applications to Submanifolds
2. Auflage 2008
ISBN: 978-0-387-74655-5
Verlag: Springer

Buch, Englisch, 208 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g

Reihe: Universitext

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.

Zielgruppe

Research

Autoren/Hrsg.

Cecil, Thomas E.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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

Über Autor(innen)

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.