Tight and Taut Submanifolds

A comprehensive 1997 survey of the field of tight and taut submanifolds.

Thomas E. Cecil (Edited by), Shiing-shen Chern (Edited by)

9780521175159, Cambridge University Press

Paperback, published 3 March 2011

368 pages
23.4 x 15.6 x 1.9 cm, 0.52 kg

Review of the hardback: ' … a comprehensive survey of the field.' European Mathematical Society

First published in 1997, this book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The book is dedicated to the memory of Nicolaas H. Kuiper; the first paper is an unfinished but insightful survey of the field of tight immersions and maps written by Kuiper himself. Other papers by leading researchers in the field treat topics such as the smooth and polyhedral portions of the theory of tight immersions, taut, Dupin and isoparametric submanifolds of Euclidean space, taut submanifolds of arbitrary complete Riemannian manifolds, and real hypersurfaces in complex space forms with special curvature properties. Taken together these articles provide a comprehensive survey of the field and point toward several directions for future research.

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 Daniel Ruberman
8. Real hypersurfaces in complex space forms Ross Niebergall and Patrick Ryan
9. Biography on tight, taut and isoparametric submanifolds Wolfgang Kühnel and Thomas E. Cecil
List of publications by Nicolaas H. Kuiper
Dissertations of N. H. Juiper's doctoral students.

Subject Areas: Differential & Riemannian geometry [PBMP]