A Hamiltonian approach to the cohomogeneity one Ricci soliton equations

TL;DR

This paper reformulates cohomogeneity one Ricci soliton equations as a Hamiltonian system, explores conserved quantities, and derives explicit formulas for certain non-Kähler Ricci solitons in five dimensions.

Contribution

It introduces a Hamiltonian framework for these equations, enabling new insights and explicit solutions for non-Kähler Ricci solitons.

Findings

Hamiltonian formulation of Ricci soliton equations

Identification of conserved quantities and superpotentials

Explicit formulas for five-dimensional non-Kähler Ricci solitons

Abstract

We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not of K\"ahler type in five dimensions.