Vol. 97, No. 1, 1981

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Manifolds admitting taut hyperspheres

James J. Hebda

Vol. 97 (1981), No. 1, 119–124
Abstract

The definition of taut submanifolds in Euclidean space is extended to submanifolds of an arbitrary complete Riemannian manifold. Manifolds containing a tautly embedded hypersphere are characterized up to homeomorphism. Also, a partial result in this direction is proved for manifolds containing a tautly embedded sphere of arbitrary codimension.

Mathematical Subject Classification 2000
Primary: 53C40
Milestones
Received: 7 October 1980
Revised: 10 March 1981
Published: 1 November 1981
Authors
James J. Hebda