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

zbMATH Open1293.53059arXiv1009.1160MaRDI QIDQ374058

Rafael Torres

Publication date: 25 October 2013

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Abstract: In this paper, first we consider the existence and non-existence of Einstein metrics on the topological 4-manifolds $$ (for $kin11,13,14,15,16,17,18$) by using the idea of Ru{a}sdeaconu and c{S}uvaina (2009) and the constructions in Park, Park, and Shin (arXiv:0906.5195v2) and in Park, Park, and Shin (2009). 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 Ishida (2008).

Full work available at URL: https://arxiv.org/abs/1009.1160

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zbMATH Keywords

Einstein metricsexotic smooth structures

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Differentiable structures in differential topology (57R55)

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