On Four-Dimensional Anti-self-dual Gradient Ricci Solitons
By Xiuxiong Chen, Yuanqi Wang. 2011
95 citations recorded by the source corpus.
In this note we prove that any four-dimensional half-conformally flat gradient steady Ricci soliton must be either isometric to the Bryant’s soliton (up to a scaling), or with zero Ricci curvature. We also classify four-dimensional half-conformally flat gradient shrinking Ricci solitons.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ac32ca85fd0dee9566d5a14c1c9564b56a6c5601
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature (2021, unknown): “In the shrinking case, classification results for gradient Ricci solitons have been obtained by many authors under various curvature conditions on the Weyl tensor, e.g., [7; 9; 10; 17; 20; 21; 24; 28; 29; 30; 31; 33; 35; 36], etc.”
- On Bach-flat gradient shrinking Ricci solitons (2011, methodology): “Very recently, by cleverly using the tensor D ijk , X. Chen and Y. Wang [13] have shown that 4-dimensional half-conformally flat gradient shrinking Ricci solitons are either Einstein, or locally conformally flat.”
- Rotational symmetry of self-similar solutions to the Ricci flow (2012, result): “roof. We note that several authors have obtained uniqueness results for the Bryant soliton and its higher dimensional counterparts under various additional assumptions. We refer to [4], [5], [6], and [8] for details. In this paper, we prove the uniqueness of the Bryant soliton under a noncollapsing ”
- Critical point equation on four‐dimensional compact manifolds (2014, methodology): “1 of [6] to conclude that T ≡ 0 at q, which finishes the proof of the lemma.”