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

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 $k\in 11,13,14,15,16,17,18$) by using the idea of Răsdeaconu and Şuvaina (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).

Added references

References in corpus (4)

• Einstein metrics and the number of smooth structures on a four-manifold
• The Normalized Ricci Flow on Four-Manifolds and Exotic Smooth Structures
• Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds
• Surfaces of general type with $p_g=1$ and $q=0$

Cited by in corpus (1)

• Surfaces of general type with $p_g=1$ and $q=0$