Seven dimensional cohomogeneity one manifolds with nonnegative curvature

2017/05/25 by Verdiani, Luigi, Ziller, Wolfgang
#53C20 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.09032

Abstract

We show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature, unless it admits one with positive curvature. As a consequence, the classification of nonnegatively curved cohomogeneity one manifolds in dimension 7 is reduced to only one further family of candidates

Related

• Cohomogeneity one manifolds with quasipositive curvature
• Classification of Cohomogeneity One Manifolds in Low Dimensions
• Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry
• New Examples of Obstructions to Non-Negative Sectional Curvatures in Cohomogeneity One Manifolds
• Nonnegative Curvature on Low Dimensional Cohomogeneity One Manifolds