The construction of negatively Ricci curved manifolds

Gao, Laiyuan

doi:10.1007/bf01455986

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Deformation Of Metric2

The Construction Of the Ricci-positive Riemannian Metrics1

Introduction1

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2011

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Cited by 17 publications

(8 citation statements)

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“…Remark 3. In [17] Theorem 4 was proved for negative Ricci curvature, but the proof is valid for positive Ricci curvature. In addition, we will need to know slightly more about the construction used in the proof of Theorem 4.…”

Section: The Construction Of the Ricci-positive Riemannian Metricsmentioning

confidence: 99%

On the moment-angle manifolds of positive Ricci curvature

Bazaikin

Matvienko

2011

Sib Math J

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Section: The Construction Of the Ricci-positive Riemannian Metricsmentioning

confidence: 99%

On the moment-angle manifolds of positive Ricci curvature

Bazaikin

Matvienko

2011

Sib Math J

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“…Our construction is a generalization of the one given by Gao in [17]. In [17], a given metric with negative Ricci curvature is deformed into another negative Ricci curvature metric by local modification about a closed curve.…”

Section: Deformation Of Metricmentioning

confidence: 99%

“…In [17], a given metric with negative Ricci curvature is deformed into another negative Ricci curvature metric by local modification about a closed curve. This method is an important ingredient in the proof of a result due to Gao-Yau, which says that every closed 3-manifold M admits a metric g with Ricc(g) < 0, (see [18]).…”

Section: Deformation Of Metricmentioning

confidence: 99%

Critical Exponent of Negatively Curved Three Manifolds

Hou¹

2003

Glasgow Math. J.

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Abstract. We prove that for a negatively pinched (−b 2 ≤ K ≤ −1) topologically tame 3-manifoldM/Γ , all geometrically infinite ends are simply degenerate. And if the limit set of Γ is the entire boundary sphere at infinity, then the action of Γ on the boundary sphere is ergodic with respect to harmonic measure, and the Poincaré series diverges when the critical exponent is 2.2000 Mathematics Subject Classification. 57M50, 57M60.

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“…We must also mention the deformation result of Gao appearing in [2]. He showed that given two Ricci-negative metrics defined in (at least) a tubular neighbourhood of an embedded circle, one of the metrics can be deformed (within Ricci-negativity) to agree with the other metric in some smaller tubular neighbourhood, provided the 1-jets of the metric agree at all points on the circle.…”

Section: Introductionmentioning

confidence: 99%