6 papers
Inhomogeneous Einstein metrics on complex projective spaces
Gonzalo Cao-Labora, Alberto Rodríguez-Vázquez
The only Einstein metrics currently known on complex projective spaces are homogeneous: the Fubini-Study metric, arising via the Hopf fibration; and, in odd complex dimensions, Zil…
The index of symmetry and homogeneous fibrations
Ángel Cidre-Díaz, Carlos E. Olmos, Alberto Rodríguez-Vázquez
We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogen…
Totally geodesic submanifolds of the homogeneous nearly Kähler 6-manifolds and their G2-cones
Juan Manuel Lorenzo-Naveiro, Alberto Rodríguez-Vázquez
In this article we classify totally geodesic submanifolds of homogeneous nearly Kähler 6-manifolds, and of the G2-cones over these 6-manifolds. To this end, we develop new techniqu…
Positive curvature on products of spheres and their quotients via intermediate fatness
Jason DeVito, Miguel Domínguez-Vázquez, David González-Álvaro +1
We construct metrics of positive intermediate Ricci curvature, , on closed manifolds of dimensions 10, 11, 12, 13 and 14, including $\mathbb{S}^6\tim…
Totally geodesic submanifolds and polar actions on Stiefel manifolds
Claudio Gorodski, Andreas Kollross, Alberto Rodríguez-Vázquez
We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove…
A nonisoparametric hypersurface with constant principal curvatures
Alberto Rodríguez-Vázquez
In this note we construct an explicit example of a (compact) conformally flat Riemannian manifold which admits a totally geodesic foliation of codimension one with no isoparametric…