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Totally Geodesic Submanifolds and Polar Actions on Stiefel Manifolds

Year: 2024
Type: article
Abstract: 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.
DOI: 10.1007/s12220-024-01855-8
Language: English
Open Access status: hybrid
Estimated APC paid: $3,090
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
Awards: G1080052004, G3480869486, Totally geodesic submanifolds and mean curvature flow in the presence of symmetry, G5080475149, G549060987, G5504558992, Polar actions on symmetric spaces of non-compact type, G6033112984, G6102875433, G7084143925, G7168513008, G7447860732
OpenAlex ID: W4405371307
FWCI: 0.382
Cites: 32
Cited by: 2
Related to: 10