Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778373 | Advances in Mathematics | 2017 | 46 Pages |
Abstract
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 â¥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 â¥8.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Peng Lu, Y.K. Wang,