Ricci solitons: the equation point of view

By Manolo Eminenti, G. Nave, Carlo Mantegazza. 2008

171 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/b8b440a4ac05463e61dc64062f0dd4196e3e776c

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. Huaihuo Cao
3. A. G. Setti
4. S. Pigola
5. Ovidiu Munteanu
6. M. Rigoli
7. Lu Wang
8. Brett Kotschwar

In Astronomy and Astrophysics

1. Michele Rimoldi
2. Huaihuo Cao
3. A. G. Setti
4. S. Pigola
5. Ovidiu Munteanu
6. Lu Wang
7. W. Wylie
8. N. Šešum

In Geometry and Topology

1. Michele Rimoldi
2. Huaihuo Cao
3. A. G. Setti
4. S. Pigola
5. Lu Wang
6. Ovidiu Munteanu
7. M. Rigoli
8. W. Wylie

Citations in the corpus

• On the classification of gradient Ricci solitons (2007, methodology): “When M is compact Theorem 1.2 was established using similar techniques by Eminenti, LaNave, and Mantegazza in [ 12 ].”
• On Ricci solitons of cohomogeneity one (2008, background): “[ 18 ] have then observed that this fact immediately implies that compact Ricci solitons with constant scalar curvature must be trivial, i.e.”
• Gradient estimates for a nonlinear parabolic equation on complete non-compact Riemannian manifolds (2009, methodology): “For gradient Ricci solitons, we have the fundamental formulas [ 6 ]”
• On Gradient Ricci Solitons (2009, methodology): “Using a technique developed in the compact setting by [11], Petersen and Wylie have obtained [28] the same classification of complete locally conformally flat gradient shrinking solitons assuming only an integral bound of the Ricci curvature: (1.”
• On Gradient Ricci Solitons with Symmetry (2007, unknown): “In fact, in the proof all we use about cohomogeneity one is a much weaker condition on f we call recti…ability which we will discuss in section 3. (Also recall that the work of Bohm and Wilking [3] implies that every compact shrinking gradient Ricci soliton with nonnegative curvature operator is a q”
• Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, background): “Also, from [16], [26], [30], [38], [43], [46], and [53], it follows that the only complete nonflat shrinking solitons of vanishing Weyl tensor (even harmonic Weyl tensor) in dimensions n ≥ 4 are finite quotients of the standard metrics on S or Sn−1 × R.”
• On Locally Conformally Flat Gradient Shrinking Ricci Solitons (2008, methodology): “Remark 1.1. In this case, the problem has also been studied by M. Eminenti, G. La Nave and C. Mantegazza [ ELM06 ] using a different method.”
• On the geometry of gradient einstein-type manifolds (2014, unknown): “[25], [28], [39], [22], [38], [48], [37], [40], [10], [7], [14], [42], [11], [13], [8], [6], [33], [5] and references therein).”
• Rigidity of shrinking Ricci solitons (2011, background): “2 posed in [8].”
• Ricci almost solitons (2010, methodology): “This is the same philosophy used, for instance, in [4,22].”
• A remark on compact Ricci solitons (2008, background): “Nontrivial compact Ricci solitons only exist in dimensions ≥ 4( cf. [10,12]) and they must have positive scalar curvature (Scal > 0) [8], which is constant if and only if the soliton is trivial since � LX g� 2 = 2div(cX −Ric(X, · )) + dScal(X ). Moreover, the Weyl tensor of a compact nontrivial Ricc”
• RIGIDITY OF GRADIENT RICCI SOLITONS (2007, background): “We can further take a quotient N ×Γ Rk, where Γ acts freely on N and by orthogonal transformations on Rk (no translational components) to get a flat vector bundle over a base that is Einstein and with f = λ2 d 2 where d is the distance in the flat fibers to the base.”
• Remarks on non-compact gradient Ricci solitons (2009, methodology): “We shall also use the next computations concerning the scalar curvature of a gradient Ricci soliton; [3], [11].”