Smooth structures, normalized Ricci flows, and finite cyclic groups
Smooth structures, normalized Ricci flows, and finite cyclic groups
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DOI：
10.1007/s10455-008-9136-6
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发表时间：
2009-05
影响因子：
0.7
通讯作者：
M. Ishida;I. Şuvaina
中科院分区：
文献类型：
--
作者：
M. Ishida;I. Şuvaina
A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors [Ishida, The normalized Ricci flow on four-manifolds and exotic smooth structures; Şuvaina, Einstein metrics and smooth structures on non-simply connected 4-manifolds] we prove that for any finite cyclic group, whered> 1, there exist infinitely many compact topological 4-manifolds, with fundamental group, which admit at least one smooth structure for which non-singular solutions of the normalized Ricci flow exist, but also admit infinitely many distinct smooth structures for whichnonon-singular solution of the normalized Ricci flow exists. We show that there are no non-singular-equivariant,d> 1, solutions to the normalized Ricci flow on appropriate connected sums ofand.
