Small four-manifolds without non-singular solutions of normalized Ricci flows

Masashi Ishida

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


It is known [6] that connected sums X#K3#(σg × σh)#l1(S1×S3)#l2CP2 satisfy the Gromov-Hitchin-Thorpe type inequality, but can not admit non-singular solutions of the normal- ized Ricci flow for any initial metric, where σg × σh is the product of two Riemann surfaces of odd genus, l1, l2 > 0 are sufficiently large positive integers, g, h > 3 are also sufficiently large positive odd integers, and X is a certain irreducible symplectic 4-manifold. These exmples are closely related with a conjecture of Fang, Zhang and Zhang [10]. In the current article, we point out that there still exist 4-manifolds with the same property even if l1 = l2 = 0 and g = h = 3. The topology of these new examples are smaller than that of previously known examples.

Original languageEnglish
Pages (from-to)609-622
Number of pages14
JournalAsian Journal of Mathematics
Issue number4
Publication statusPublished - 2014


  • Four-manifold
  • Non-singular solution
  • Ricci flow

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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