Riemannian geometry has today become a vast and important subject. This new book of
Marcel Berger sets out to introduce readers to most of the living topics of the field and …

Manifolds with non-negative sectional curvature have been of interest since the beginning of
global Riemannian geometry, as illustrated by the theorems of Bonnet-Myers, Synge, and …

It is well known that Lie groups and homogeneous spaces provide a rich source of
interesting examples for a variety of geometric aspects. Likewise it is often the case that …

It was recently observed by M. Xu and J. Wolf that there is a gap in Berard Bergery's
classification of odd-dimensional positively curved homogeneous spaces. Since this …

Isometry groups of homogeneous spaces with positive sectional curvature Page 1 Differential
Geometry and its Applications 14 (2001) 57–78 57 North-Holland www.elsevier.com/locate/difgeo …

The symmetry rank of a Riemannian manifold is the rank of the isometry group. We
determine precisely which closed simply connected 5-manifolds admit positively curved …

A π 1-invariant torus-action on a manifold M is a T k-action on the universal covering which
extends to the action of a semi-direct product π 1 (M)× ρ T k. In particular, the T k-action is …

A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold
with positive sectional curvature has positive Euler characteristic. We prove this conjecture …

Global Riemannian Geometry generalizes the classical Euclidean, Spherical, and
Hyperbolic geometries. One of the major challenges in this area is to understand how local …

Our main theorem asserts that for all odd n≥3 and 0< δ≤1, there exists a small constant,
i(n,δ)>0, such that if a simply connected n-manifold, M, with vanishing second Betti number …