On locally conformally flat gradient steady Ricci solitons

Cao, Huai-Dong; Chen, Qiang

doi:10.1090/s0002-9947-2011-05446-2

Cited by 138 publications

(192 citation statements)

References 21 publications

Supporting

Mentioning

183

Contrasting

Order By: Relevance

“…This classification result, including also the three-dimensional LCF case, was first obtained recently by H.-D. Cao and Q. Chen [6].…”

Section: The Classification Of Steady and Shrinking Gradient Lcf Riccsupporting

confidence: 75%

See 1 more Smart Citation

The Evolution of the Weyl Tensor under the Ricci Flow

Catino¹,

Mantegazza²

2011

Ann. inst. Fourier

View full text Add to dashboard Cite

show abstract

“…This classification result, including also the three-dimensional LCF case, was first obtained recently by H.-D. Cao and Q. Chen [6].…”

Section: The Classification Of Steady and Shrinking Gradient Lcf Riccsupporting

confidence: 75%

“…We follow now the argument in the proof of Theorem 1.1 in [6]. We recall the following splitting result (see [11,Chapter 7,Section 3]) which is a consequence of Hamilton's strong maximum principle for systems in [17].…”

Section: Singularities Of Ricci Flow With Bounded Weyl Tensormentioning

confidence: 99%

The Evolution of the Weyl Tensor under the Ricci Flow

Catino¹,

Mantegazza²

2011

Ann. inst. Fourier

View full text Add to dashboard Cite

show abstract

“…Following the soliton proof in [13], we consider the Weyl tensor in order to get control on the other eigenvalues of P . In the next proposition we record the decomposition of Q in terms of the Weyl tensor.…”

Section: Corollary 71 If (M G W) Is a (λ N + M)-einstein Manifolmentioning

confidence: 99%

On the classification of warped product Einstein metrics

Petersen

Wylie

2012

Communications in Analysis and Geometry

114

164

View full text Add to dashboard Cite

In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the m-quasi Einstein equation, but we will also call it the (λ, n + m)-Einstein equation. In this paper we extend the work of Case-Shu-Wei and some earlier work of Kim-Kim to allow the base to have non-empty boundary. This is a natural case to consider since a manifold without boundary often occurs as a warped product over a manifold with boundary, and in this case we get some interesting new canonical examples. We also derive some new formulas involving curvatures that are analogous to those for the gradient Ricci solitons. As an application, we characterize warped product Einstein metrics when the base is locally conformally flat.

show abstract

“…[7], [8], [9], and [11]. Moreover, T. Ivey [14] has constructed examples of Ricci solitons which are not rotationally symmetric.…”

Section: Introductionmentioning

confidence: 99%