Work

Hopf fibrations and totally geodesic submanifolds

Year: 2025

Type: article

Abstract: We classify totally geodesic submanifolds in Hopf–Berger spheres, which constitute a special family of homogeneous spaces diffeomorphic to spheres constructed via Hopf fibrations. As a byproduct of our investigations, we have discovered very intriguing examples of totally geodesic submanifolds: totally geodesic submanifolds isometric to real projective spaces, uncountably many isometric but non-congruent totally geodesic submanifolds, and a totally geodesic submanifold that is not extrinsically homogeneous. Remarkably, all these examples arise in certain Hopf–Berger spheres with positive curvature.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1606

Authors: Carlos Enrique Olmos, Alberto Rodríguez-Vázquez

Institutions: Universidad Nacional de Córdoba, Université Libre de Bruxelles

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Fonds Wetenschappelijk Onderzoek, Xunta de Galicia, Vlaamse regering, Agencia Estatal de Investigación