Smooth Structures and Normalized Ricci Flows on Non-Simply Connected Four-Manifolds

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dc.creatorIshida, Masashi
dc.creatorSuvaina, Ioana
dc.date2008-08-03
dc.date.accessioned2026-07-07T09:54:29Z
dc.date.available2026-07-07T09:54:29Z
dc.descriptionA 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, we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on 4-manifolds with non-trivial fundamental group and the relation with the smooth structures. For example, we prove that, for any finite cyclic group ${\mathbb Z}_{d}$, where $d>1$, there exists a compact topological 4-manifold $X$ with fundamental group ${\mathbb Z}_{d}$, which admits at least one smooth structure for which non-singular solutions of the normalized Ricci flow exist, but also admits infinitely many distinct smooth structures for which {\it no} non-singular solution of the normalized Ricci flow exists. Related non-existence results on non-singular solutions are also proved. Among others, we show that there are no non-singular $\ZZ_d-$equivariant solutions to the normalized Ricci flow on appropriate connected sums of $\bcp ^2$s and $\cpb $s ($d>1$).
dc.identifierhttps://arxiv.org/abs/0808.0316
dc.identifierhttp://arxiv.org/abs/0808.0316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166329
dc.subjectDifferential Geometry
dc.titleSmooth Structures and Normalized Ricci Flows on Non-Simply Connected Four-Manifolds
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