Ricci flow, Einstein metrics and space forms

Approximating Ricci solitons and quasi-Einstein metrics on toric surfaces

We present a general numerical method for investigating prescribed Ricci curvature problems on toric Kähler manifolds. This method is applied to two generalisations of Einstein metrics, namely Ricci solitons and quasi-Einstein metrics. We begin by recovering the Koiso–Cao soliton and the Lü–Page–Pope quasi-Einstein metrics on CP2]CP (in both cases the metrics are known explicitly). We also find...

Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds

dL(Mo,M1) = inf[llogdil/l + Ilogdil/-II], f where I: Mo -+ MI is a homeomorphism and dil I is the dilatation of I given by dill = SUPXt#2 dist(f(x l ), l(x2))/ dist(x1 ,x2). If Mo and MI are not homeomorphic, define dL(Mo,M1) = +00. Gromov [20] proves the remarkable result that the space of compact Riemannian manifolds L(A,t5 ,D) of sectional curvature IKI :::; A, injectivity radius i M 2: t5 >...

On Einstein metrics, normalized Ricci flow and smooth structures on 3CP#kCP

In this paper, first we consider the existence and nonexistence of Einstein metrics on the topological 4-manifolds 3CP#kCP, the connected sum of CP 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 ...

0 Ricci flow on Kähler - Einstein surfaces

Ricci Flow on Kähler-einstein Manifolds