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Ancient solutions of the Ricci flow on bundles
Journal article

Ancient solutions of the Ricci flow on bundles

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 ≥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.

Authors

Lu P; Wang YK

Journal

Advances in Mathematics, Vol. 318, , pp. 411–456

Publisher

Elsevier

Publication Date

October 1, 2017

DOI

10.1016/j.aim.2017.08.011

ISSN

0001-8708

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