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.

Author Bio

Jeremy Mann graduated from Johns Hopkins University in the Spring of 2012, with a major in Mathematics. He will be attending Notre Dame's PhD program in Mathematics starting Fall of 2013, where he plans to study geometric analysis. His paper grew out of an independent study under the supervision of Dr. Jian Ge.