Positively curved deformations of invariant Riemannian metrics

Nonnegatively and Positively Curved Invariant Metrics on Circle Bundles

We derive and study necessary and sufficient conditions for an S-bundle to admit an invariant metric of positive or nonnegative sectional curvature. In case the total space has an invariant metric of nonnegative curvature and the base space is odd dimensional, we prove that the total space contains a flat totally geodesic immersed cylinder. We provide several examples, including a connection me...

ON THE LIFTS OF SEMI-RIEMANNIAN METRICS

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

Sobolev Metrics on the Riemannian Manifold of All Riemannian Metrics

On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L-metric as decribed first by [10]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition...

An Infinite Family of Distinct 7-manifolds Admitting Positively Curved Riemannian Structures

On One Family of 13-dimensional Closed Riemannian Positively Curved Manifolds

In the present paper we describe one family of closed Riemannian manifolds with positive sectional curvature. Now the list of known examples is not large (for instance, all known manifolds with dimension > 24 are diffeomorphic to compact rank one symmetric spaces) (we restrict ourselves only by pointing out simply connected manifolds) : 1) Berger described all normally homogeneous closed positi...