On $δ$-homogeneous Riemannian manifolds
| dc.creator | Berestovskii, V. N. | |
| dc.creator | Nikonorov, Yu. G. | |
| dc.date | 2006-11-20 | |
| dc.date | 2007-02-09 | |
| dc.date.accessioned | 2026-07-07T07:45:34Z | |
| dc.date.available | 2026-07-07T07:45:34Z | |
| dc.description | We study in this paper previously defined by V.N. Berestovskii and C.P. Plaut $δ$-homogeneous spaces in the case of Riemannian manifolds. Every such manifold has non-negative sectional curvature. The universal covering of any $δ$-homogeneous Riemannian manifolds is itself $δ$-homogeneous. In turn, every simply connected Riemannian $δ$-homogeneous manifold is a direct metric product of an Euclidean space and compact simply connected indecomposable homogeneous manifolds; all factors in this product are itself $δ$-homogeneous. We find different characterizations of $δ$-homogeneous Riemannian spaces, which imply that any such space is geodesic orbit (g.o.) and every normal homogeneous Riemannian manifold is $δ$-homogeneous. The g.o. property and the $δ$-homogeneity property are inherited by closed totally geodesic submanifolds. Then we find all possible candidates for compact simply connected indecomposable Riemannian $δ$-homogeneous non-normal manifolds of positive Euler characteristic and a priori inequalities for parameters of the corresponding family of Riemannian $δ$-homogeneous metrics on them (necessarily two-parametric). We prove that there are only two families of possible candidates: non-normal (generalized) flag manifolds $SO(2l+1)/U(l)$ and $Sp(l)/U(1)\cdot Sp(l-1)$, $l\geq 2$, investigated earlier by W. Ziller, H. Tamaru, D.V. Alekseevsky and A. Arvanitoyeorgos. At the end we prove that the corresponding two-parametric family of Riemannian metrics on $SO(5)/U(2)=Sp(2)/U(1)\cdot Sp(1)$ satisfying the above mentioned (strict!) inequalities, really generates $δ$-homogeneous spaces, which are not normal and are not naturally reductive with respect to any isometry group. | |
| dc.description | 40 pages, some results are strengthened, new references are added | |
| dc.identifier | https://arxiv.org/abs/math/0611557 | |
| dc.identifier | http://arxiv.org/abs/math/0611557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123571 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C20 (primary), 53C25, 53C35 (secondary) | |
| dc.title | On $δ$-homogeneous Riemannian manifolds | |
| dc.type | text |