Curvature and symmetry of Milnor spheres.
Closed Geodesics on Homogeneous Spaces.
The Free Loop Space of Globally Symmetric Spaces.
The Jacobi equation on naturally reductive compact Riemannian homogeneous spaces.
Symmetric spaces and strongly isotropy irreducibel spaces.
Minimal isometric immersions of spherical space forms in spheres.
On the volume of a unit vector field on the three-sphere.
On normal homogeneous Einstein manifolds
On the topology of positively curved Bazaikin spaces
We explore some aspects of the topology of the family of 13-dimensional Bazaikin spaces. Using the computation of their homology rings, Pontryagin classes and linking forms, we show that there is only one Bazaikin space that is homotopy equivalent to a homogeneous space, i.e., the Berger space. Moreover, it is easily shown that there are only finitely many Bazaikin spaces in each homeomorphism type and that there are only finitely many positively curved ones for a given cohomology ring. In fact,...
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case when both are equal to two, where existence of non-negatively curved metrics is known.
Editorial note : “Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres”
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