Rigidity of shrinking Ricci solitons

By M. Fernández-López, E. García‐Río. 2011

106 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/26da79623674bdb35c9e18d2187f62830a69dc02

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Michele Rimoldi
2. Qiang Chen
3. A. G. Setti
4. Chenxu He
5. S. Pigola
6. M. Rigoli
7. Huaihuo Cao
8. Lu Wang

In Astronomy and Astrophysics

1. Michele Rimoldi
2. Qiang Chen
3. Chenxu He
4. Lu Wang
5. Huaihuo Cao
6. A. G. Setti
7. S. Pigola
8. M. Rigoli

In Geometry and Topology

1. Michele Rimoldi
2. Qiang Chen
3. Chenxu He
4. Lu Wang
5. Huaihuo Cao
6. A. G. Setti
7. M. Rigoli
8. S. Pigola

Citations in the corpus

• On the classification of warped product Einstein metrics (2010, background): “2(n−1) (g⊙g)(X,Y,Z,∇ρ) = − m−1 n−1 (g⊙g)(X,Y,Z,P(∇w)). These two equations combine to give the desired identity. This gives us the following corollary, a similar lemma for Ricci solitons is proven in [FLGR]. Corollary 7.5. If (M,g,w) is a (λ,n+ m)-Einstein manifold and has harmonic Weyl tensor then,”
• On Bach-flat gradient shrinking Ricci solitons (2011, methodology): “In the latter case, by the rigidity theorem of Fern´andez-L´opez and Garc´ıa-R´ıo [16] and Munteanu-Sesum [20] for harmonic Weyl tensor, ( M n , g ij , f ) is either Einstein or isometric to a finite quotient of of ) the product of an Einstein manifold N n − k with the Gaussian shrinking soliton R k…”
• Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, methodology): “The work of Fernández-López and Garćıa-Ŕıo [32] and Munteanu-Sesum [41] has since extended this classification to shrinkers of harmonic Weyl tensor.”
• Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature (2021, unknown): “In particular, Fernández-López and García-Río [21] together with Munteanu and Sesum [28] proved that any n -dimensional complete gradient shrinker with harmonic Weyl tensor is rigid, i.e., it is isometric to a (finite) quotient of N × (cid:82) k , the product soliton of an Einstein manifold N of…”
• On locally conformally flat gradient steady Ricci solitons (2009, background): “Fernández-López and Garćıa-Rı́o [10] showed, by a different argument, that for shrinking solitons with harmonic Weyl tensor the gradient of any potential function is an eigenvector of the Ricci tensor.”
• Ricci almost solitons (2010, background): “Garcı́aRı́o, [7], the authors extend Zhang’s classification result to complete shrinkers with harmonic Weyl tensor.”