Tight and Taut Submanifolds [Paperback]

A comprehensive 1997 survey of the field of tight and taut submanifolds.Tight and taut submanifolds form an important special class of surfaces in the general field of differential geometry. This subject has been studied intensively by differential geometers since the 1950's. This book contains six in-depth articles by leading experts in the field as well as an extensive bibliography of the entire field. Taken together, these articles provide a comprehensive survey of the field and point toward several directions for future research. The book is intended for researchers in the field and as a reference for libraries.Tight and taut submanifolds form an important special class of surfaces in the general field of differential geometry. This subject has been studied intensively by differential geometers since the 1950's. This book contains six in-depth articles by leading experts in the field as well as an extensive bibliography of the entire field. Taken together, these articles provide a comprehensive survey of the field and point toward several directions for future research. The book is intended for researchers in the field and as a reference for libraries.Tight and taut manifolds form an important and special class of surfaces within differential geometry. This book contains in-depth articles by experts in the field as well as an extensive and comprehensive bibliography. This survey will open new avenues for further research and will be an important addition to any geometer's library.Preface; 1. Remembering Nicolaas Kuiper Thomas F. Banchoff; 2. Roever lectures in geometry Nicolaas H. Kuiper; 3. Smooth and polyhedral tight immersions Thomas F. Banchoff; 4. Tightness for smooth and polyhedral immersions of the real projective plane with one handle Davide P. Cervone; 5. Taut and Dupin submanifolds Thomas E. Cecil; 6. Taut immersions into complete Riemannian manifolds Chuu-Lian Terng and Gudlaugur Thorbergsson; 7. Null-homotopic embedded spheres of codimension one Dl“ž