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

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

Abstract
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.

Author information

California Institute of Technology -- Mathematics, 1200 E California Blvd, Pasadena, CA 91125
rtorresr@caltech.edu