Curvature, triameter, and beyond

Grove, Karsten; Markvorsen, Steen

doi:10.1090/S0273-0979-1992-00308-7

Curvature, triameter, and beyond
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by Karsten Grove and Steen Markvorsen PDF

Bull. Amer. Math. Soc. 27 (1992), 261-265 Request permission

Abstract:

In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of invariants, the first term of which is the usual diameter, and illustrate the role of these global shape invariants in a number of recognition problems.

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