The equilateral Dimension of a riemannian manifold is the maximum number of distinct equidistant points. In the first half of this paper we will give upper bounds for the equilateral dimension of certain Riemannian Manifolds. In the second half of the paper we will introduce a new metric invariant, called the equilateral length, which measures size of the equilateral dimension. This will then be used in the recognition program in Riemannian geometry, which seeks to identify certain Riemannian manifolds by way of metric invariants such as diameter, extent, or packing radius.
Professor Jian Ge, Department of Mathematics, Johns Hopkins University
"Equilateral Dimension of Riemannian Manifolds with Bounded Curvature,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 8.
Available at: http://scholar.rose-hulman.edu/rhumj/vol14/iss1/8