# The canonical shrinking soliton associated to a Ricci flow

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- On quasi-conformally flat weakly Ricci symmetric manifolds. Jana, S. K.; Shaikh, A. A. // Acta Mathematica Hungarica;May2007, Vol. 115 Issue 3, p197
The object of the present paper is to study quasi-conformally flat weakly Ricci symmetric manifolds.

- Geometric Convergence of the KÃ¤hler-Ricci Flow on Complex Surfaces of General Type. Bin Guo; Jian Song; Weinkove, Ben // IMRN: International Mathematics Research Notices;2016, Vol. 2016 Issue 18, p5652
We show that on smooth minimal surfaces of general type, the KÃ¤hler-Ricci flow starting at any initial KÃ¤hler metric converges in the Gromov-Hausdorff sense to a KÃ¤hler- Einstein orbifold surface. In particular, the diameter of the evolving metrics is uniformly bounded for all time, and...

- Geometry of Ricci Solitons. Huai-Dong Cao // Chinese Annals of Mathematics;Apr2006, Vol. 27 Issue 2, p121
Ricci solitons are natural generalizations of Einstein metrics on one hand, and are special solutions of the Ricci flow of Hamilton on the other hand. In this paper we survey some of the recent developments on Ricci solitons and the role they play in the singularity study of the Ricci flow.

- A local version of Bando's theorem on the real-analyticity of solutions to the Ricci flow. Kotschwar, Brett L. // Bulletin of the London Mathematical Society;Feb2013, Vol. 45 Issue 1, p153
It is a theorem of Bando that if g(t) is a solution to the Ricci flow on a compact manifold M, then (M, g(t)) is real-analytic for each t > 0. In this note, we extend his result to smooth solutions on open domains U âŠ‚ M.

- Ricci solitons on Lorentzian manifolds with large isometry groups. Batat, W.; Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. // Bulletin of the London Mathematical Society;Dec2011, Vol. 43 Issue 6, p1219
We show that Lorentzian manifolds whose isometry group is of dimension at least Â½n(nâˆ’1)+1 admit different vector fields resulting in expanding, steady and shrinking Ricci solitons. Moreover, it is proved that those Ricci solitons are gradient (only) in the steady case. This provides...

- Ricci Solitons and Gradient Ricci Solitons in a Kenmotsu Manifolds. Chand De, Uday; Yoshio Matsuyama // Southeast Asian Bulletin of Mathematics;2013, Vol. 37 Issue 5, p691
The object of the present paper is to study a Kenmotsu manifold admitting Ricci solitons and gradient Ricci solitons.

- A simple proof on the non-existence of shrinking breathers for the Ricci flow. Hsu, Shu-Yu // Calculus of Variations & Partial Differential Equations;Sep2006, Vol. 27 Issue 1, p59
Suppose M is a compact n-dimensional manifold, n= 2, with a metric g ij ( x, t) that evolves by the Ricci flow ? t g ij = -2 R ij in Mï¿½ (0, T). We will give a simple proof of a recent result of Perelman on the non-existence of shrinking breather without using the logarithmic Sobolev...

- Curvature homogeneous Lorentzian three-manifolds. Calvaruso, Giovanni // Annals of Global Analysis & Geometry;Aug2009, Vol. 36 Issue 1, p1
We study three-dimensional curvature homogeneous Lorentzian manifolds. We prove that for all Segre types of the Ricci operator, there exist examples of nonhomogeneous curvature homogeneous Lorentzian metrics in $${\mathbb R^3}$$ .

- Metrics of positive Ricci curvature on bundles. Belegradek, Igor; Wei, Guofang // IMRN: International Mathematics Research Notices;2004, Vol. 2004 Issue 57, p3079
We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector bundle over a compact manifold of nonnegative Ricci...