A remark on compact Ricci solitons

By M. Fernández-López, E. García‐Río. 2008

119 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/66a2214a8d748f4e0c097b4de8c5b59f659152b8

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Rigidity of shrinking Ricci solitons (2011, background): “Compact Ricci solitons not given by a Killing vector are shrinking and moreover any complete shrinking Ricci soliton whose norm is bounded is necessarily compact [9].”
The Bakry–Emery Ricci tensor and its applications to some compactness theorems (2012, background): “Instead of the assumption | φ |≤ k given in Theorem 1, we can assume that g(∇φ,∇φ) ∈ C∞(M) has an upper bound: In [2], Fernández-López and García-Río proved that, if (M, g) admits a vector field V satisfying the inequality Ric + LV g ≥ c > 0 where LV denotes the Lie derivative, and √ g(V, V ) has an”
Recent Progress on Ricci Solitons (2009, result): “In the compact case, the result was first proved by Derdzinski [41] and Fernádez-López and Garćıa-Rı́o [49] (see also a different proof by EminentiLa Nave-Mantegazza [44]).”
Remarks on non-compact gradient Ricci solitons (2009, background): “Triviality of expanders under L∞ conditions and scalar curvature estimates It is known, [4], that a complete, shrinking Ricci soliton (M, 〈, 〉 ,X) satisfying |X| ∈ L∞ must be compact.”
Complete gradient shrinking Ricci solitons have finite topological type (2007, background): “In this note we are concerned with complete Riemannian manifold (M, g) satisfying that Ric+Hess(f) ≥ λg for some constant λ > 0 and f ∈ C∞(M), i.e., whose Bakry-Émery Ricci tensor is bounded below by λ in the sense of [7].”
Ricci solitons and concurrent vector fields (2014, background): “[10, 14]) and the other looking at its influence on its geometry (see e.”
Ricci almost solitons (2010, result): “We shall prove the next theorem, which extends results obtained in [4, 5, 17, 32].”
Geometry of Complete Gradient Shrinking Ricci Solitons (2009, result): “In the compact case, this result was proved by8 Derdzinski [16], and Fernádez-López and Garćıa-Rı́o [20] (see also a different proof by Eminenti-La Nave-Mantegazza [17]).”
Ricci solitons: the equation point of view (2008, background): “We are also aware of a preprint [15] of Fernández–López andGarcía–Ríowhere they show that the first fundamental group has to be finite.”