Cohomogeneity one manifolds with positive Ricci curvature

Grove, Karsten; Ziller, Wolfgang

doi:10.1007/s002220200225

Cited by 115 publications

(153 citation statements)

References 26 publications

Supporting

Mentioning

151

Contrasting

Unclassified

Order By: Relevance

“…Therefore we must only consider the case in which K + is a subgroup strictly between H and G. Following the tables given in [Grove and Ziller 2002], we address these cases one by one. We first list the diagram, then the corresponding action.…”

Section: In Our Case This Impliesmentioning

confidence: 99%

Classification of cohomogeneity one manifolds in low dimensions

Hoelscher¹

2010

Pacific J. Math.

View full text Add to dashboard Cite

A cohomogeneity one manifold is a manifold whose quotient by the action of a compact Lie group is one-dimensional. Such manifolds are of interest in Riemannian geometry in the context of nonnegative sectional curvature, as well as in other areas of geometry and in physics. We classify compact simply connected cohomogeneity one manifolds in dimensions 5, 6 and 7. We also show that all such manifolds admit metrics of nonnegative sectional curvature, with the possible exception of two families of manifolds.

show abstract

Section: In Our Case This Impliesmentioning

confidence: 99%

Classification of cohomogeneity one manifolds in low dimensions

Hoelscher¹

2010

Pacific J. Math.

View full text Add to dashboard Cite

show abstract

“…It is well-known that if G acts transitively, then it preserves a metric of Ric ≥ 0, which has Ric > 0 if and only if π 1 (M ) is finite. It was shown in [GZ02] that the same is true for cohomogeneity one actions. By [GPT98], M admits a G-invariant metric of Ric > 0 if the action is free, G is connected, M/G admits a metric of Ric > 0, and π 1 (M ) is finite.…”

Section: Introductionmentioning

confidence: 68%

Nonnegative Curvature, Symmetry and Fundamental Group

Belegradek

2004

Geometriae Dedicata

View full text Add to dashboard Cite

show abstract

“…We mention that in the case of Ricci curvature one has the positive result that every cohomogeneity one manifold carries an invariant metric with non-negative Ricci curvature, and with positive Ricci curvature if and only if the fundamental group is finite [43].…”

Section: Compact Examples With Non-negative Curvaturementioning

confidence: 99%