Ancient Solutions on Bundles with Non-abelian Structural Group

Abstract

We generalize the ancient solutions of the Ricci flow on certain principal $\mathrm{SO}(3)$ bundles over compact quaternionic Kähler manifolds constructed by Bakas, Kong, and Ni to certain $R{P}^3$ fibre bundles over a product of two compact quaternionic Kähler manifolds. The ancient solutions are of Type I, $\kappa$-noncollapsed, and have positive Ricci curvature. Analogous solutions on even-dimensional non-Kählerian bundle spaces are also constructed.

33 pages