53 citations · 76 across the 16 of their papers we have counts for
22 papers
Hopf fibrations and totally geodesic submanifolds
Carlos E. Olmos, Alberto Rodríguez-Vázquez
We classify totally geodesic submanifolds in Hopf-Berger spheres, which constitute a special family of homogeneous spaces diffeomorphic to spheres constructed via Hopf fibrations.…
The structure of homogeneous Riemannian manifolds with nullity
Antonio J. Di Scala, Carlos E. Olmos, Francisco Vittone
We find new conditions that the existence of nullity of the curvature tensor of an irreducible homogeneous space imposes on the Lie algebra of and on the…
The Index Conjecture for Symmetric Spaces
Jurgen Berndt, Carlos Olmos
In 1980, Onishchik introduced the index of a Riemannian symmetric space as the minimal codimension of a (proper) totally geodesic submanifold. He calculated the index for symmetric…
Cones and Cartan geometry
Antonio J. Di Scala, Carlos E. Olmos, Francisco Vittone
We show that the extended principal bundle of a Cartan geometry of type , endowed with its extended connection , is isomorphic to the pri…
The index of exceptional symmetric spaces
Jürgen Berndt, Carlos Olmos, Juan Sebastián Rodríguez
The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold (Onishchik, 1980). There is a conjecture by the first two authors for…
Homogeneous Riemannian manifolds with non-trivial nullity
Antonio J. Di Scala, Carlos E. Olmos, Francisco Vittone
We develop a general theory for irreducible homogeneous spaces , in relation to the nullity of their curvature tensor. We construct natural invariant (different and inc…