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This book contains six in-depth articles by leading
experts in the field and an extensive bibliography.
It is dedicated
to the memory of Nicolaas H. Kuiper, and the first paper is
an unfinished but insightful exposition of the subject of tight
immersions and maps, written by Kuiper. Other papers survey
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 constant principal curvatures. Taken
together these articles provide a comprehensive survey of the field
and point toward several directions for future research.