Totally geodesic submanifolds of the complex and the quaternionic 2-Grassmannians
| dc.creator | Klein, Sebastian | |
| dc.date | 2007-09-17 | |
| dc.date.accessioned | 2026-07-07T13:17:21Z | |
| dc.date.available | 2026-07-07T13:17:21Z | |
| dc.description | In this article, I classify the totally geodesic submanifolds in the complex 2-Grassmannians and in the quaternionic 2-Grassmannians. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic submanifolds in Riemannian symmetric spaces of rank 2, published by Chen and Nagano (B.-Y. Chen, T. Nagano, "Totally geodesic submanifolds of symmetric spaces, II", Duke Math. J. 45 (1978), 405--425) is incomplete. For example, G_2(H^n) with n >= 7 contains totally geodesic submanifolds isometric to a HP^2, its metric scaled such that the minimal sectional curvature is 1/5; they are maximal in G_2(H^7). Also G_2(C^n) with n >= 6 contains totally geodesic submanifolds which are isometric to a CP^2 contained in the HP^2 mentioned above; they are maximal in G_2(C^6). Neither submanifolds are mentioned in the cited paper by Chen and Nagano. | |
| dc.identifier | https://arxiv.org/abs/0709.2644 | |
| dc.identifier | http://arxiv.org/abs/0709.2644 | |
| dc.identifier | Trans. Amer. Math. Soc. 361 (2009), 4927-4967 | |
| dc.identifier | doi:10.1090/S0002-9947-09-04699-6 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231089 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C35 (Primary); 53C17 (Secondary) | |
| dc.title | Totally geodesic submanifolds of the complex and the quaternionic 2-Grassmannians | |
| dc.type | text |