On Ricci solitons of cohomogeneity one

By A. Dancer, Mckenzie Y. Wang. 2008

157 citations recorded by the source corpus.

We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansätze of cohomogeneity one to produce new explicit examples of complete Kähler Ricci solitons of expanding, steady and shrinking types. These solitons are foliated by hypersurfaces which are circle bundles over a product of Fano Kähler–Einstein manifolds or over coadjoint orbits of a compactly connected semisimple Lie group.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cef7c66a18e5aa748e551ebe7fe2f88278996b0f

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, background): “Excluding products and otherwise locally reducible metrics, to the authors’ knowledge, the only complete noncompact examples in the literature belong either to the family of Kähler-Ricci solitons on complex line bundles constructed by Feldman-Ilmanen-Knopf [31] or to those of their generalizations ”
Geometry of Complete Gradient Shrinking Ricci Solitons (2009, background): “ar curvature but the Ricci curvature changes sign. The simplest such example is deﬁned on the tautological line bundle O(−1) of CP1, the blow-up of C2 at the origin. Remark 1.1. Recently, Dancer-Wang [15] produced new examples of rotationally symmetric compact and complete noncompact gradient Kahler”
On Gradient Ricci Solitons with Symmetry (2007, unknown): “D G ] 2 4 Se p 20 08”
Recent Progress on Ricci Solitons (2009, background): “er family (doubly warped product metrics) of gradient expanding solitons on Rm+1 × N, where Nn (n ≥ 2) is an Einstein manifold with positive scalar curvature. Example 1.10. Very recently, Dancer-Wang [39] produced new examples of gradient shrinking, steady and expanding Kahler solitons on bundles ov”