The classification of $δ$-homogeneous Riemannian manifolds with positive Euler characteristic
| dc.creator | Berestovskii, V. N. | |
| dc.creator | Nikitenko, E. V. | |
| dc.creator | Nikonorov, Yu. G. | |
| dc.date | 2009-03-03 | |
| dc.date.accessioned | 2026-07-07T12:48:35Z | |
| dc.date.available | 2026-07-07T12:48:35Z | |
| dc.description | The authors give a short survey of previous results on $δ$-homogeneous Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with non-negative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable $δ$-homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds $Sp(l)/U(1)\cdot Sp(l-1)=\mathbb{C}P^{2l-1}$, $l\geq 2$, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval $(1/16, 1/4)$. This implies very unusual geometric properties of the adjoint representation of $Sp(l)$, $l\geq 2$. Some unsolved questions are suggested. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0903.0457 | |
| dc.identifier | http://arxiv.org/abs/0903.0457 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222108 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C20 (Primary), 53C25, 53C35 (Secondary) | |
| dc.title | The classification of $δ$-homogeneous Riemannian manifolds with positive Euler characteristic | |
| dc.type | text |