The classification of $δ$-homogeneous Riemannian manifolds with positive Euler characteristic

dc.creatorBerestovskii, V. N.
dc.creatorNikitenko, E. V.
dc.creatorNikonorov, Yu. G.
dc.date2009-03-03
dc.date.accessioned2026-07-07T12:48:35Z
dc.date.available2026-07-07T12:48:35Z
dc.descriptionThe 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.description17 pages
dc.identifierhttps://arxiv.org/abs/0903.0457
dc.identifierhttp://arxiv.org/abs/0903.0457
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222108
dc.subjectDifferential Geometry
dc.subject53C20 (Primary), 53C25, 53C35 (Secondary)
dc.titleThe classification of $δ$-homogeneous Riemannian manifolds with positive Euler characteristic
dc.typetext

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