A numerical study of cohomogeneity one manifolds

Abstract

This dissertation explores numerical solutions for the cohomogeneity one Einstein and Ricci soliton equations when the principal orbits are SU(3)/T^2 and Sp(3)/Sp(1)^3. We present new numerical evidence for steady, expanding solitons as well as Einstein metrics with positive scalar curvature. In the case of steady solitons we produced a one-parameter family of solutions. In the expanding case, we generated a two-parameter family of solutions and in particular in the negative Einstein case we generated a one-parameter family of solutions. In the compact Einstein case we found numerical evidence for an in nite number of Einstein metrics.