Abstract

In this paper, we study the Ricci-Bourguignon flow on higher dimensional classical Heisenberg nilpotent Lie groups and construct a solution of this flow on Heisenberg and quaternion nilpotent Lie groups. In the end, we investigate the deformation of spectrum and length spectrum on compact nilmanifolds obtained of Heisenberg and quaternion nilpotent Lie groups.

Keywords: Ricci-Bouguignon flow; Heisenberg type; Lie group.

MSC: 53C44, 22E25

Pages:  124$-$137     

Volume  72 ,  Issue  2 ,  2020