Totally Geodesic Submanifolds and Polar Actions on Stiefel Manifolds
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 that the orbits of polar actions are lifts of polar actions on the corresponding Grassmannian. In the case of cohomogeneity one actions we are able to obtain a classification for all real, complex and quaternionic Stiefel manifolds of k-frames.
Authors
- Andreas Kollross (ORCID: https://orcid.org/0000-0002-5591-4227)
- Alberto Rodríguez-Vázquez (ORCID: https://orcid.org/0000-0002-5748-7556)
- Cláudio Gorodski (ORCID: https://orcid.org/0000-0002-2965-0889)
Institutions
- University of Stuttgart (DE)
- Université Libre de Bruxelles (BE)
- Universidade de São Paulo (BR)
Publication Details
- Journal
- Journal of Geometric Analysis
- Published
- 2024-12-13
- DOI
- https://doi.org/10.1007/s12220-024-01855-8
- Citations
- 1
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.97
Funders
- European Commission
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Fonds Wetenschappelijk Onderzoek
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia
- Xunta de Galicia
- European Regional Development Fund
- Agencia Estatal de Investigación
- HORIZON EUROPE Marie Sklodowska-Curie Actions