## Abstract

It is known [6] that connected sums X#K3#(σ_{g} × σ_{h})#l_{1}(S^{1}×S^{3})#l_{2}CP^{2} 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 σ_{g} × σ_{h} is the product of two Riemann surfaces of odd genus, l_{1}, l_{2} > 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 l_{1} = l_{2} = 0 and g = h = 3. The topology of these new examples are smaller than that of previously known examples.

Original language | English |
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Pages (from-to) | 609-622 |

Number of pages | 14 |

Journal | Asian Journal of Mathematics |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

## Keywords

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

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics