Communications in Analysis and Geometry

Volume 28 (2020)

Number 1

Ancient solutions on bundles with non-abelian structural group

Pages: 141 – 187



Peng Lu (Department of Mathematics, University of Oregon, Eugene, Or., U.S.A.)

Y. K. Wang (Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)


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 $\mathbb{RP}^3$ 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.

P.L. is partially supported by Simons Foundation through Collaboration Grant 229727. Y.K.W. is partially supported by NSERC Grant No. OPG0009421.

Received 22 October 2016

Accepted 23 October 2017

Published 12 March 2020