Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature

On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature

In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.

On the Geometry of Cohomogeneity One Manifolds with Positive Curvature

There are very few known examples of manifolds with positive sectional curvature. Apart from the compact rank one symmetric spaces, they exist only in dimensions 24 and below and are all obtained as quotients of a compact Lie group equipped with a biinvariant metric under an isometric group action. They consist of certain homogeneous spaces in dimensions 6, 7, 12, 13 and 24 due to Berger [Be], ...

on cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature

in this paper, we give a classification of non simply connected seven dimensional reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. we characterize the acting groups and describe the orbits. the first and second homo-topy groups of the orbits have been presented as well.

Arithmetic Manifolds of Positive Scalar Curvature

Simply Connected Manifolds of Positive Scalar Curvature

Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M of dimension > 5, the vanishing of a(M) is sufficient for the existence of a Riemannian metric on M with positive scalar curvature. We prove this conjecture using techniques from stable homotopy th...