Kähler-Ricci flow and Kähler-Ricci solitons

2007 ◽  
pp. 55-125
Author(s):  
Bennett Chow ◽  
Sun-Chin Chu ◽  
David Glickenstein ◽  
Christine Guenther ◽  
James Isenberg ◽  
...  
Keyword(s):  
Ricci Flow ◽  
Ricci Solitons

scholarly journals Non-Kähler Ricci flow singularities modeled on Kähler–Ricci solitons

2019 ◽  
Vol 15 (2) ◽  
pp. 749-784 ◽  
Author(s):  
James Isenberg ◽  
Dan Knopf ◽  
Nataša Šešum
Keyword(s):  
Ricci Flow ◽  
Ricci Solitons

Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions

2014 ◽  
Vol 11 (4) ◽  
pp. 2529-2568
Author(s):  
Christoph Böhm ◽  
Jorge Lauret ◽  
McKenzie Wang
Keyword(s):  
Ricci Flow ◽  
Einstein Metrics ◽  
Ricci Solitons

scholarly journals Singular Ricci Solitons and Their Stability under the Ricci Flow

2015 ◽  
Vol 40 (12) ◽  
pp. 2123-2172 ◽  
Author(s):  
Spyros Alexakis ◽  
Dezhong Chen ◽  
Grigorios Fournodavlos
Keyword(s):  
Ricci Flow ◽  
Ricci Solitons

scholarly journals Homogeneous Ricci solitons

2015 ◽  
Vol 2015 (699) ◽  
Author(s):  
Michael Jablonski
Keyword(s):  
Lie Groups ◽  
Ricci Flow ◽  
Isometry Group ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Solvable Lie Groups ◽  
Compact Case ◽  
Group Of Isometries ◽  
Simply Connected ◽  
Special Case

AbstractIn this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we show that it is isometric to a solvsoliton. Moreover, unless the manifold is flat, it is necessarily simply-connected and diffeomorphic to ℝIn the general case, we prove that homogeneous Ricci solitons must be semi-algebraic Ricci solitons in the sense that they evolve under the Ricci flow by dilation and pullback by automorphisms of the isometry group. In the special case that there exists a transitive semi-simple group of isometries on a Ricci soliton, we show that such a space is in fact Einstein. In the compact case, we produce new proof that Ricci solitons are necessarily Einstein.Lastly, we characterize solvable Lie groups which admit Ricci soliton metrics.

scholarly journals Stability of compact Ricci solitons under Ricci flow

2015 ◽  
Vol 39 ◽  
pp. 490-500 ◽  
Author(s):  
Mina VAGHEF ◽  
Asadollah RAZAVI
Keyword(s):  
Ricci Flow ◽  
Ricci Solitons

scholarly journals Transverse Kähler–Ricci Solitons of Five-Dimensional Sasaki–Einstein Spaces Yp,q and T1,1

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 330
Author(s):  
Mihai Visinescu
Keyword(s):  
Ricci Flow ◽  
Vector Fields ◽  
Ricci Solitons ◽  
Explicit Solutions ◽  
Reeb Vector ◽  
Transverse Structure ◽  
Flow Equations ◽  
Einstein Spaces ◽  
Sasakian Structures ◽  
Sasaki Manifolds

We investigate the deformations of the Sasaki–Einstein structures of the five-dimensional spaces T 1 , 1 and Y p , q by exploiting the transverse structure of the Sasaki manifolds. We consider local deformations of the Sasaki structures preserving the Reeb vector fields but modify the contact forms. In this class of deformations, we analyze the transverse Kähler–Ricci flow equations. We produce some particular explicit solutions representing families of new Sasakian structures.

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