2016/06/03 by Lu, Peng, Wang, Y. K.
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1606.01112
We generalize the circle bundle examples of ancient solutions of the Ricci flow discovered by Bakas, Kong, and Ni to a class of principal torus bundles over an arbitrary finite product of Fano Kähler-Einstein manifolds studied by Wang and Ziller in the context of Einstein geometry. As a result, continuous families of κ-collapsed and κ-noncollapsed ancient solutions of type I are obtained on circle bundles for all odd dimensions ≥ 7. In dimension 7 such examples moreover exist on pairs of homeomorphic but not diffeomorphic manifolds. Continuous families of κ-collapsed ancient solutions of type I are also obtained on torus bundles for all dimensions ≥ 8.