Editorial note : “Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres”

More precisely in Section 2 we prove Theorem 1.1; for that we first derive estimates on the geometric quantities in perturbed metric, then with a blow down procedure we get that

To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compact base in fact

Our results are in contrast to the homogeneous case, where all compact man- ifolds admit an invariant metric of non-negative curvature, and they leave the clas- sification

In [6] the most simple non-trivial case of the cohomogeneity one Einstein equations is investigated: It is assumed that the space of G- invariant metrics on the principal orbit type

Grossman’s estimate [8] of the distance from a totally geo- desic submanifold to its focal cut locus on compact manifolds of strictly positive sectional curvature

In other words, although we have started from a threedimensional problem without a potential in the interior of the domain under consid- eration, in the limit, in a

This result is used to prove that if Z TM is an exotic n-sphere which does not bound a spin manifold, then the only possible compact connected transformation groups of

Proposition 2.1 If Theorem 1.2 holds for constant curvature spheres, it holds for any closed, positively curved, Riemannian, locally symmetric space.. We will proceed by