arXiv subjects

Juan Manuel Lorenzo-Naveiro

Publications and source records attributed to Juan Manuel Lorenzo-Naveiro.

4 recordsLinked to original sources

arXiv2026

Totally geodesic submanifolds of the homogeneous nearly Kähler 6-manifolds and their G2-cones

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 techniques for the study of totally geodesic submanifolds of analytic Riemannian manifolds, naturally reductive homogeneous spaces, and Riemannian cones. In particular, we obtain an example of a totally geodesic submanifold with self-intersections in a simply connected homogeneous space.

math.DG↗

arXiv2026

Polar homogeneous foliations on symmetric spaces of rank one

We classify polar homogeneous foliations on rank one symmetric spaces of noncompact type up to orbit equivalence.

math.DG↗

arXiv2024

Codimension two polar homogeneous foliations on symmetric spaces of noncompact type

We classify homogeneous polar foliations of codimension two on irreducible symmetric spaces of noncompact type up to orbit equivalence. Any such foliation is either hyperpolar or the canonical extension of a polar homogeneous foliation on a rank one symmetric space.

math.DG↗

arXiv2022

Sections of polar actions

In this short note we provide an elementary proof of the folklore result in the theory of isometric Lie group actions on Riemannian manifolds asserting that sections of polar actions are totally geodesic.

math.DG↗