TY - JOUR
T1 - Small four-manifolds without non-singular solutions of normalized Ricci flows
AU - Ishida, Masashi
N1 - Publisher Copyright:
© 2014 International Press.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Four-manifold
KW - Non-singular solution
KW - Ricci flow
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U2 - 10.4310/AJM.2014.v18.n4.a3
DO - 10.4310/AJM.2014.v18.n4.a3
M3 - Article
AN - SCOPUS:84921633542
VL - 18
SP - 609
EP - 622
JO - Asian Journal of Mathematics
JF - Asian Journal of Mathematics
SN - 1093-6106
IS - 4
ER -