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∈11,13,14,15,16,17,18) by using the idea of R\u{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).

On Einstein metrics, normalized Ricci flow and smooth structures on 3ℂℙ2 # kℂℙ2

Torres Ruiz, Rafael
2013-01-01

Abstract

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∈11,13,14,15,16,17,18) by using the idea of R\u{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).
2013
19
2013
179
188
http://nyjm.albany.edu/j/2013/19-12v.pdf
https://arxiv.org/abs/1009.1160
Torres Ruiz, Rafael
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32784
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