Geometry of Hypersurfaces

Thomas E. Cecil is professor of mathematics at the College of Holy Cross in Worcester, MA, USA. His primary research interests are in differential geometry, in particular, submanifolds.Patrick J. Ryan is Emeritus professor of mathematical sciences at McMaster University in Hamilton, Ontario, Canada. His primary research interests are in Geometry, in particular, the characterization and classification of hypersurfaces in real and complex space forms.

• Preface.- 1. Introduction.- 2. Submanifolds of Real Space Forms.- 3. Isoparametric Hypersurfaces.- 4. Submanifolds in Lie Sphere Geometry.- 5. Dupin Hypersurfaces.- 6. Real Hypersurfaces in Complex Space Forms.- 7. Complex Submanifolds of CPn and CHn.- 8. Hopf Hypersurfaces.- 9. Hypersurfaces in Quaternionic Space Forms.- Appendix A. Summary of Notation.- References.- Index.

“This 600-page book is the result of the authors’ efforts to provide a detailed presentation of the present day differential geometry of hypersurfaces in real, complex, and quaternionic space forms. … A summary of the frequently used notations and an index of notions are included. The book is an essential contribution to the progress of the theory of hypersurfaces.” (Radu Miron, zbMATH 1331.53001, 2016)