Book contents
- Frontmatter
- Contents
- Preface
- Remembering Nicolaas Kuiper
- Geometry in Curvature Theory
- Tight Submanifolds, Smooth and Polyhedral
- Tightness for Smooth and Polyhedral Immersions of the Projective Plane with One Handle
- Taut and Dupin Submanifolds
- Taut Immersions into Complete Riemannian Manifolds
- Null-Homotopic Embedded Spheres of Codimension One
- Real Hypersurfaces in Complex Space Forms
- Bibliography on Tight, Taut and Isoparametric Submanifolds
- List of Publications
- Dissertations of N. H. Kuiper's Doctoral Students
Geometry in Curvature Theory
Published online by Cambridge University Press: 25 June 2025
Book contents
- Frontmatter
- Contents
- Preface
- Remembering Nicolaas Kuiper
- Geometry in Curvature Theory
- Tight Submanifolds, Smooth and Polyhedral
- Tightness for Smooth and Polyhedral Immersions of the Projective Plane with One Handle
- Taut and Dupin Submanifolds
- Taut Immersions into Complete Riemannian Manifolds
- Null-Homotopic Embedded Spheres of Codimension One
- Real Hypersurfaces in Complex Space Forms
- Bibliography on Tight, Taut and Isoparametric Submanifolds
- List of Publications
- Dissertations of N. H. Kuiper's Doctoral Students
Summary
This article is based on the Roever Lectures in Geometry given by Kuiper at Washington University, St. Louis, in January 1986. Although incomplete, it is an excellent exposition of the topics it does cover, starting with elementary versions of the notion of tightness and going through the analysis of topsets, the classification in low dimensions, the notions of total curvature for curves and surfaces in space, homological notions of tightness, the Morse inequalities, and Poincare polynomials. It contains a detailed proof of Kuiper's remarkable result that a tight two-dimensional surface substantially immersed in ℝ5 must be a Veronese surface.
EDITORS’ NOTE. At the time of Kuiper's death in December, 1994, this paper existed in the form of an unfinished typescript. For inclusion in this volume, it was edited by Thomas Banchoff, Thomas Cecil, Wolfgang Kühnel, and Silvio Levy. A few Editors’ Notes such as this one were included, mostly pointing to additional references. Several minor typos were corrected and the numbering was normalized for ease of reference; thus Sections 5 and 6 of the manuscript were renumbered 4 and 5, since there was no Section 4. The present illustrations were made by Christine Heinitz and by Levy, based on Kuiper's hand drawings.
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- Tight and Taut Submanifolds , pp. 1 - 50Publisher: Cambridge University PressPrint publication year: 1997
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