Non-singular solutions to the normalized Ricci flow equation |
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| Authors: | Fuquan Fang Yuguang Zhang Zhenlei Zhang |
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| Institution: | (1) Department of Mathematics, Capital Normal University, Beijing, People’s Republic of China;(2) Nankai Institute of Mathematics, Weijin Road 94, Tianjin, 300071, People’s Republic of China |
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| Abstract: | In this paper, we study non-singular solutions to Ricci flow on a closed manifold of dimension at least 4. Amongst other things
we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t > 0 with uniformly bounded sectional curvature, then the Euler characteristic  . Moreover, the 4-manifold satisfies one of the followings
| (i) |
M is a shrinking Ricci soliton;
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| (ii) |
M admits a positive rank F-structure;
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| (iii) |
the Hitchin–Thorpe type inequality holds |
where  (resp.  ) is the Euler characteristic (resp. signature) of M.
The first author was supported by a NSF Grant of China and the Capital Normal University. |
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| Keywords: | |
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