The Ricci-Bourguignon flow on Heisenberg and quaternion Lie groups

TL;DR

This paper investigates the Ricci-Bourguignon flow on higher-dimensional Heisenberg and quaternion Lie groups, constructing solutions and analyzing spectral deformations on associated nilmanifolds.

Contribution

It provides explicit solutions to the Ricci-Bourguignon flow on specific nilpotent Lie groups and studies spectral deformation effects on related compact nilmanifolds.

Findings

Constructed solutions of the Ricci-Bourguignon flow on Heisenberg and quaternion Lie groups

Analyzed the deformation of spectrum and length spectrum on associated nilmanifolds

Enhanced understanding of geometric flow behavior on nilpotent Lie groups

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.