Deformation of spectrum and length spectrum on some compact nilmanifolds under the Ricci flow

In this article we study the eigenvalue variations of Heisenberg and quaternion Lie groups under the Ricci flow and we investigate the deformation of some characteristics of compact nilmanifolds $\Gamma\setminus N$ under the Ricci flow, where $N$ is a simply connected $2$-step nilpotent Lie group with a left invariant metric and $\Gamma$ is a discrete cocompact subgroup of $N$, in particular Heisenberg and quaternion Lie groups.