Painlevé analysis of the Bryant Soliton

Abstract

We carry out a Painlevé analysis of the systems of differential equations corresponding to the steady and the expanding, rotationally symmetric, gradient Ricci solitons on ${\mathbb{R}}^n$. For the steady case, dimensions of the form $n=k^2+1$ are singled out, with dimensions 2, 5, and 10 being particularly distinguished. Only dimension 2 is singled out for the expanding soliton.

arXiv commentSome minor corrections in the introduction and conclusion as well as more references added. 12 Pages

References in corpus (2)

• Spacetime Energy Decreases under World-sheet RG Flow
• A Hamiltonian approach to the cohomogeneity one Ricci soliton equations

Cited by in corpus (1)

• A Hamiltonian approach to the cohomogeneity one Ricci soliton equations