Central conjugate locus of 2-step nilpotent Lie groups

Abstract

The goals of this article are twofold : 1) to compute the conjugate locus of a geodesic that lies in the center of a simply connected, 2-step nilpotent Lie group with a left invariant metric 2) compare the isometry types of two such nilpotent Lie groups whose conjugate loci for central geodesics are "the same" in a suitable sense. The first goal is achieved. The second is elusive, but we obtain a partial result.