On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$

Details On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$ On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$

2010-09-06

arxiv.org/abs/1009.1160v1

Mathematics

Differential Geometry

Scientific paper

In this paper, first we consider the existence and non-existence of Einstein metrics on the topological 4-manifolds $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$ (for $k \in \{11, 13, 14, 15, 16, 17, 18\}$) by using the idea of \cite{[RS]} and the constructions in \cite{[PPS]} and in \cite{[PPS1]}. Then, we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on the exotic smooth structures of these topological manifolds by employing the obstruction developed in \cite{[MI]}.

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