New York Journal of Mathematics
Volume 19 (2013) 179-188


Rafael Torres

On Einstein metrics, normalized Ricci flow and smooth structures on 3CP2 # k\bar{CP2}

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Published: May 28, 2013
Keywords: Q-Gorenstein smoothings, surfaces of general type, exotic smooth structures, Einstein metrics
Subject: Primary 53C25; Secondary 57R55

In this paper, first we consider the existence and nonexistence of Einstein metrics on the topological 4-manifolds 3CP2 # k \bar{CP2}, the connected sum of CP2 with both choices of orientation, by using the idea of Răsdeaconu-Şuvaina, 2009, and the constructions in Park-Park-Shin, 2013. Then, we study the existence or nonexistence of nonsingular solutions of the normalized Ricci flow on the exotic smooth structures of these topological manifolds by employing the obstruction developed in Ishida, 2008.

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California Institute of Technology -- Mathematics, 1200 E California Blvd, Pasadena, CA 91125