Totally geodesic submanifolds of the complex quadric

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dc.creatorKlein, Sebastian
dc.date2006-03-07
dc.date.accessioned2026-07-07T09:19:08Z
dc.date.available2026-07-07T09:19:08Z
dc.descriptionIn this article, relations between the root space decomposition of a Riemannian symmetric space of compact type and the root space decompositions of its totally geodesic submanifolds (symmetric subspaces) are described. These relations provide an approach to the classification of totally geodesic submanifolds in Riemannian symmetric spaces. In this way a classification of the totally geodesic submanifolds in the complex quadric $Q^m := \SO(m+2)/(\SO(2) \times \SO(m))$ is obtained. It turns out that the earlier classification of totally geodesic submanifolds of $Q^m$ by Chen and Nagano is incomplete: in particular a type of submanifolds which are isometric to 2-spheres of radius $\tfrac{1}{2}\sqrt{10}$, and which are neither complex nor totally real in $Q^m$, is missing.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0603167
dc.identifierhttp://arxiv.org/abs/math/0603167
dc.identifierDifferential Geom. Appl. 26 (2008), 79-96
dc.identifierdoi:10.1016/j.difgeo.2007.11.004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154278
dc.subjectDifferential Geometry
dc.subject53C35 (Primary); 53C17
dc.titleTotally geodesic submanifolds of the complex quadric
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