Thu, 02 May 2024
17:00 -
18:00
L4
Cohomogeneity one Ricci solitons and Hamiltonian formalism
Qiu Shi Wang
( Oxford)
Abstract
A Riemannian manifold is said to be of cohomogeneity one if there is a Lie group acting on it by isometries with principal orbits of codimension one. On such manifolds, the Ricci soliton equation simplifies to a system of ODEs, which can be considered as a Hamiltonian system. Various conserved quantities, such as superpotentials, can then be defined to find cases in which the system is explicitly integrable.
There is a considerable body of work, primarily due to A. Dancer and M. Wang, on the analogous procedure for the Einstein equation.
In this talk, I will introduce the abovementioned methods and illustrate with examples their usefulness in finding explicit formulae for Ricci solitons. I will also discuss the classification of superpotentials.
There is a considerable body of work, primarily due to A. Dancer and M. Wang, on the analogous procedure for the Einstein equation.
In this talk, I will introduce the abovementioned methods and illustrate with examples their usefulness in finding explicit formulae for Ricci solitons. I will also discuss the classification of superpotentials.