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1997 (Publication #79)

Geometry in Curvature Theory

posthumous article by Nicolaas Kuiper, completed in collaboration with Thomas Cecil in "Tight and Taut Submanifolds" Eds. S.-S.Chern and T. Cecil, Cambridge University Press (1997), 1-50.

ABSTRACT

This article is based on the Roever Lecture 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.